stability of peakons the peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods we give a very simple proof of the orbital stability of the peakons in the h1 norm 2000 john wiley sons inc

rational recursion operators for integrable differential difference equations in this paper we introduce the concept of prehamiltonian pairs of difference operators demonstrate their connections with nijenhuis operators and give a criteria for the existence of weakly nonlocal inverse recursion operators for differential difference equations we begin with a rigorous setup of the problem in terms of the skew field of rational pseudo difference operators over a difference field with a zero characteristic subfield of constants and the principal ideal ring of matrix rational pseudo difference operators in particular we give a criteria for a rational operator to be weakly nonlocal a difference operator is called prehamiltonian if its image is a lie subalgebra with respect to the lie bracket on the difference field two prehamiltonian operators form a prehamiltonian pair if any linear combination of them is prehamiltonian then we show that a prehamiltonian pair naturally leads to a nijenhuis operator and a nijenhuis operator can be represented in terms of a prehamiltonian pair this provides a systematic method to check whether a rational operator is nijenhuis as an application we construct a prehamiltonian pair and thus a nijenhuis recursion operator for the differential difference equation recently discovered by adler and postnikov the nijenhuis operator obtained is not weakly nonlocal we prove that it generates an infinite hierarchy of local commuting symmetries we also illustrate our theory on the well known examples including the toda the ablowitz ladik and the kaup newell differential difference equations

analyticity of periodic traveling free surface water waves with vorticity we prove that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a ow with a real analytic vorticity must be real analytic provided the wave speed exceeds the horizontal uid velocity throughout the ow the real analyticity of each streamline be

a note on well posedness for camassa holm equation in this note we investigate the problem of well posedness for a shallow water equation with data having critical regularity our results are based on the use of besov spaces b2 rs which generalize the sobolev spaces hs with critical index s 3 2

stability in the energy space of the sum of n peakons for a modified camassa holm equation with higher order nonlinearity considered herein is the orbital stability in the energy space h1 r of a decoupled sum of n peakons for a modified camassa holm equation with higher order nonlinearity the equation studied here admits single peakon and multi peakons based on our obtained result of the stability of a single peakon and then combining modulation argument with monotonicity of the local energy h1 norm we get the stability of the sum of n peakons considered herein is the orbital stability in the energy space h1 r of a decoupled sum of n peakons for a modified camassa holm equation with higher order nonlinearity the equation studied here admits single peakon and multi peakons based on our obtained result of the stability of a single peakon and then combining modulation argument with monotonicity of the local energy h1 norm we get the stability of the sum of n peakons

multilinear estimates for periodic kdv equations and applications we prove an endpoint multilinear estimate for the xs b spaces associated to the periodic airy equation as a consequence we obtain sharp local well posedness results for periodic generalized kdv equations as well as some global well posedness results below the energy norm

global weak solutions to the novikov equation abstract the existence of global weak solutions to the cauchy problem for the novikov equation is established in the space c 0 r l 0 h 1 r without the sign condition on the initial value the limit of viscous approximations for the equation is used to establish the existence of the global weak solution the key elements in our analysis include a new one sided super bound and a new higher norm estimate on the first order derivatives of the solution

non uniform dependence on initial data for the two component novikov system considered herein is the initial value problem for the two component novikov system it is shown that the solution map of this problem is not uniformly continuous in sobolev spaces hs hs 1 for s 5 2 on the line based on the well posedness result and the lifespan for this problem the method of approximate solutions is utilized

a fully supersymmetric akns theory we construct a fully supersymmetric bihamiltonian theory in four superfields admitting zero curvature and lax formulation this theory is an extension of the classical akns which can be recovered as a reduction other supersymmetric theories are obtained as reductions of the susy akns namely a nonlinear schrodinger a modified kdv and the manin radul kdv the susy nonlinear schrodinger hierarchy is related to the one of roelofs and kersten we determine its bihamiltonian and lax formulation finally we show that the susy kdv s mentioned before are related through a susy miura map

global existence for a new periodic integrable equation we establish the local well posedness for a new periodic integrable equation we show that the equation has classical solutions that blowup in finite time as well as classical solutions which exist globally in time

local well posedness and blow up criteria for a two component novikov system in the critical besov space abstract in this paper we mainly investigate the cauchy problem of a two component novikov system we first prove the local well posedness of the system in besov spaces b p r s 1 b p r s with p r 1 s max 1 1 p 3 2 by using the littlewood paley theory and transport equations theory then by virtue of logarithmic interpolation inequalities and the osgood lemma we establish the local well posedness of the system in the critical besov space b 2 1 1 2 b 2 1 3 2 moreover we present two blow up criteria for the system by making use of the conservation laws

lipschitz metric for the novikov equation we consider the lipschitz continuous dependence of solutions for the novikov equation with respect to the initial data in particular we construct a finsler type optimal transport metric which renders the solution map lipschitz continuous on bounded sets of h 1 mathbb r cap w 1 4 mathbb r although it is not lipschitz continuous under the natural sobolev metric from an energy law due to the finite time gradient blowup by an application of thom s transversality theorem we also prove that when the initial data is in an open dense subset of h 1 mathbb r cap w 1 4 mathbb r the solution is piecewise smooth this generic regularity result helps us extend the lipschitz continuous metric to the general weak solutions our method of constructing the metric can be used to treat other kinds of quasi linear equations provided a good knowledge about the energy concentration

integrable peakon equations with cubic nonlinearity we present a new integrable partial differential equation found by vladimir novikov like the camassa holm and degasperis procesi equations this new equation admits peaked soliton peakon solutions but it has nonlinear terms that are cubic rather than quadratic we give a matrix lax pair for v novikov s equation and show how it is related by a reciprocal transformation to a negative flow in the sawada kotera hierarchy infinitely many conserved quantities are found as well as a bi hamiltonian structure the latter is used to obtain the hamiltonian form of the finite dimensional system for the interaction of n peakons and the two body dynamics n 2 is explicitly integrated finally all of this is compared with some analogous results for another cubic peakon equation derived by zhijun qiao

on asymptotically equivalent shallow water wave equations abstract the integrable third order korteweg de vries kdv equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves however at quadratic order this asymptotic expansion produces an entire family of shallow water wave equations that are asymptotically equivalent to each other under a group of nonlinear non local normal form transformations introduced by kodama in combination with the application of the helmholtz operator these kodama helmholtz kh transformations are used to present connections between shallow water waves the integrable fifth order kdv equation and a generalization of the camassa holm ch equation that contains an additional integrable case the dispersion relation of the full water wave problem and any equation in this family agree to fifth order the travelling wave solutions of the ch equation are shown to agree to fifth order with the exact solution

estimating migration rates using tag recovery data tag recovery data are used to estimate migration rates among a set of strata the model formulation is a simple matrix extension of the formulation of a tag recovery experiment discussed by brownie et al 1985 statistical inference from band recovery data a handbook 2nd edition washington d c u s department of the interior estimation is more difficult because of the convolution of parameters between release and recovery and this convolution may cause estimates of the survival migration parameters to have low precision derived parameters of emigration immigration harvest derivation and overall net survival are also estimated the models are applied to estimate the migration of pacific herring among spawning grounds off the west coast of canada if animals can be re released after being recaptured the model corresponds in its migration survival components to that of arnason 1972 researches in popiulation ecology 13 97 113 this correspondence is developed leading to more efficient estimators of these parameters

modeling association among demographic parameters in analysis of open population capture recapture data we present a hierarchical extension of the cormack jolly seber cjs model for open population capture recapture data in addition to recaptures of marked animals we model first captures of animals and losses on capture the parameter set includes capture probabilities survival rates and birth rates the survival rates and birth rates are treated as a random sample from a bivariate distribution thus the model explicitly incorporates correlation in these demographic rates a key feature of the model is that the likelihood function which includes a cjs model factor is expressed entirely in terms of identifiable parameters losses on capture can be factored out of the model since the computational complexity of classical likelihood methods is prohibitive we use markov chain monte carlo in a bayesian analysis we describe an efficient candidate generation scheme for metropolis hastings sampling of cjs models and extensions the procedure is illustrated using mark recapture data for the moth gonodontis bidentata

blow up phenomena and global existence for a two component camassa holm system with an arbitrary smooth function abstract in the paper we mainly investigate blow up phenomena and global existence of strong solutions to a two component camassa holm systems with an arbitrary smooth function h for three types of smooth functions h by using a conservation law and the sign preserving property of strong solutions we obtain two new blow up results and a new global existence result for the two component system our obtained results generalize and cover the recent results in yan et al 2015 zhang and yin 2015 2016

continuous covariates in mark recapture recovery analysis a comparison of methods time varying individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured we examine three methods to incorporate time varying individual covariates of the survival probabilities into the analysis of data from mark recapture recovery experiments deterministic imputation a bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history and a conditional approach considering only the events for which the associated covariate data are completely observed the trinomial model after describing the three methods we compare results from their application to the analysis of the effect of body mass on the survival of soay sheep ovis aries on the isle of hirta scotland simulations based on these results are then used to make further comparisons we conclude that both the trinomial model and bayesian imputation method perform best in different situations if the capture and recovery probabilities are all high then the trinomial model produces precise unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate in contrast the bayesian imputation method performs substantially better when capture and recovery probabilities are low provided that the specified model of the covariate is a good approximation to the true data generating mechanism

closed form likelihoods for arnason schwarz models we provide a general framework for the computationally efficient analysis both bayesian and classical of integrated multi site recovery recapture models in the presence of individual level covariates by extending the basic arnason schwarz models and deriving closed form likelihood expressions together with corresponding sufficient statistics

bayesian estimation of movement and survival probabilities from capture recapture data summary the arnason schwarz model is usually used for estimating survival and movement probabilities of animal populations from capture recapture data the missing data structure of this capture recapture model is exhibited and summarised via a directed graph representation taking advantage of this structure we implement a gibbs sampling algorithm from which bayesian estimates and credible intervals for survival and movement probabilities are derived convergence of the algorithm is proved using a duality principle we illustrate our approach through a real example

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

global weak solutions for the novikov equation in the paper we mainly study the existence and uniqueness of global weak solutions for the novikov equation we first recall some results and definitions on strong solutions and weak solutions for the equation then we show that the equation has smooth solutions which exist globally in time provided the initial data satisfy certain sign conditions finally we prove the existence and uniqueness of global weak solutions to the equation with the initial data satisfying certain sign conditions

a generalized nonisospectral camassa holm equation and its multipeakon solutions abstract motivated by the paper of beals sattinger and szmigielski 2000 3 we propose an extension of the camassa holm equation which also admits the multipeakon solutions the novel aspect is that our approach is mainly based on classic determinant technique furthermore the proposed equation is shown to possess a nonisospectral lax pair

global weak solutions for a new periodic integrable equation with peakon solutions abstract we prove the existence of global weak solutions for a new periodic integrable equation with peakon solutions

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

well posedness global existence and blowup phenomena for a periodic quasi linear hyperbolic equation we establish the local well posedness of a recently derived model for small amplitude shallow water waves for a large class of initial data we prove global existence of the corresponding solution criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained and an existence and uniqueness result for a class of global weak solutions is also given c 1998 john wiley sons inc

some new integrable systems constructed from the bi hamiltonian systems with pure differential hamiltonian operators abstract when both hamiltonian operators of a bi hamiltonian system are pure differential operators we show that the generalized kupershmidt deformation gkd developed from the kupershmidt deformation in 10 offers an useful way to construct new integrable system starting from the bi hamiltonian system we construct some new integrable systems by means of the generalized kupershmidt deformation in the cases of harry dym hierarchy classical boussinesq hierarchy and coupled kdv hierarchy we show that the gkd of harry dym equation gkd of classical boussinesq equation and gkd of coupled kdv equation are equivalent to the new integrable rosochatius deformations of these soliton equations with self consistent sources we present the lax pair for these new systems therefore the generalized kupershmidt deformation provides a new way to construct new integrable systems from bi hamiltonian systems and also offers a new approach to obtain the rosochatius deformation of soliton equation with self consistent sources

global solutions to a special case of the generalized weakly dissipative periodic two component camassa holm system abstract we establish global well posedness to the generalized weakly dissipative periodic two component camassa holm system in some special case

well posedness and analyticity for the cauchy problem for the generalized camassa holm equation abstract in this paper we are concerned with the cauchy problem for the generalized camassa holm equation which was proposed by hakkaev and kirchev s hakkaev k kirchev local well posedness and orbital stability of solitary wave solutions for the generalized camassa holm equation comm partial differential equations 30 2005 761 781 we establish the local well posedness for a range of besov spaces moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time which extends some results of danchin r danchin a few remarks on the camassa holm equation differential integral equations 14 2001 953 988 and himonas and misiolek a himonas g misiolek analyticity of the cauchy problem for an integrable evolution equation math ann 327 2003 575 584 to more general equations

post release stratification in band recovery models brownie et al statistical inferencefrom band recovery data a handbook 2nd edition washington d c fish and wildlife service u s department of the interior 1985 present methodology for the analysis of band recovery data when all animals are assumed to behave independently and all animals are homogeneous with respect to annual survival and band recovery rates we extend these results and investigate band recovery models in cases where stratum assignment takes place after the banded animals are released usually at recovery time and each stratum may have different annual survival rates or band recovery rates or both estimation under four possible models is examined tests to distinguish among models the asymptotic power of the tests and goodness of fit tests for each model are also developed the methods are applied to band recoveries of north american mallards by flyways

the cauchy problem for a generalized camassa holm equation abstract in this paper we are concerned with the cauchy problem of the generalized camassa holm equation using a galerkin type approximation scheme it is shown that this equation is well posed in sobolev spaces h s s 3 2 for both the periodic and the nonperiodic case in the sense of hadamard that is the data to solution map is continuous furthermore it is proved that this dependence is sharp by showing that the solution map is not uniformly continuous the nonuniform dependence is proved using the method of approximate solutions and well posedness estimates moreover it is shown that the solution map for the generalized camassa holm equation is holder continuous in h r topology finally with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time

an extension of the cormack jolly seber model for continuous covariates with application to microtus pennsylvanicus recent developments in the cormack jolly seber cjs model for analyzing capture recapture data have focused on allowing the capture and survival rates to vary between individuals several methods have been developed in which capture and survival are functions of auxiliary variables that may be discrete constant over time or apply to the population as a whole but the problem has not been solved for continuous covariates that vary with both time and individual this article proposes a new method to handle such covariates by modeling changes over time via a diffusion process and using logistic functions to link the variable to the cjs capture and survival rates bayesian methods are used to estimate the model parameters the method is applied to study the effect of body mass on the survival of the north american meadow vole microtus pennsylvanicus

global conservative solutions of the camassa holm equation this paper develops a new approach in the analysis of the camassa holm equation by introducing a new set of independent and dependent variables the equation is transformed into a semilinear system whose solutions are obtained as fixed points of a contractive transformation these new variables resolve all singularities due to possible wave breaking returning to the original variables we obtain a semigroup of global solutions depending continuously on the initial data our solutions are conservative in the sense that the total energy equals a constant for almost every time

periodic solutions of the camassa holm equation based on the bilinear form since the famous work of camassa and holm various analytic techniques have been used to find the exact solutions of camassa holm ch equation and many interesting results have been found by the different methods in this paper we first give an extended bilinear form of the ch equation which contains four more free parameters than those in the results proposed in parkers finding for soliton solutions thus we construct the smooth periodic solution of the ch equation in a parametric form based on the previous work of nakumura we also show that the periodic solution degenerates into the smooth solitary wave solution by limiting behavior of is the parameter appeared from the riemann theta function

semi markov arnason schwarz models we consider multi state capture recapture recovery data where observed individuals are recorded in a set of possible discrete states traditionally the arnason schwarz model has been fitted to such data where the state process is modeled as a first order markov chain though second order models have also been proposed and fitted to data however low order markov models may not accurately represent the underlying biology for example specifying a time independent first order markov process involves the assumption that the dwell time in each state i e the duration of a stay in a given state has a geometric distribution and hence that the modal dwell time is one specifying time dependent or higher order processes provides additional flexibility but at the expense of a potentially significant number of additional model parameters we extend the arnason schwarz model by specifying a semi markov model for the state process where the dwell time distribution is specified more generally using for example a shifted poisson or negative binomial distribution a state expansion technique is applied in order to represent the resulting semi markov arnason schwarz model in terms of a simpler and computationally tractable hidden markov model semi markov arnason schwarz models come with only a very modest increase in the number of parameters yet permit a significantly more flexible state process model selection can be performed using standard procedures and in particular via the use of information criteria the semi markov approach allows for important biological inference to be drawn on the underlying state process for example on the times spent in the different states the feasibility of the approach is demonstrated in a simulation study before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis

on the solvability of the painleve vi equation a rigorous method was introduced by fokas and zhou 1992 for studying the riemann hilbert problem associated with the painleve ii and iv equations the same methodology has been applied to the painleve i iii and v equations in this paper we will apply the same methodology to the painleve vi equation we will show that the cauchy problem for the painleve vi equation admits in general a global meromorphic solution in t furthermore the special solution which can be written in terms of a hypergeometric function is obtained via solving the special case of the riemann hilbert problem

the cauchy problem for the integrable novikov equation in this paper we consider the cauchy problem for the integrable novikov equation by using the littlewood paley decomposition and nonhomogeneous besov spaces we prove that the cauchy problem for the integrable novikov equation is locally well posed in the besov space b p r s with 1 max 1 1 p 3 2 in particular when u 0 is an element of b p r s boolean and h l with 1 max 1 1 p 3 2 for all t is an element of 0 t we have that vertical bar vertical bar u t vertical bar vertical bar h l vertical bar vertical bar u 0 vertical bar vertical bar h l we also prove that the local well posedness of the cauchy problem for the novikov equation fails in b 2 3 2 infinity c 2012 elsevier inc all rights reserved

a remark on admissible triples for the generalized kdv equation abstract in this paper we give a condition of type l x p l t q under which the solution u t of the generalized kdv equation satisfies for any 1 1 for any admissible triples p 1 q 1 1 the following inequality d x 1 u t l x p 1 l t q 1 c d x u 0 l 2 we also present a global well posedness result in some spaces of admissible triples

existence of blow up solutions in the energy space for the critical generalized kdv equation from these conservation laws h appears as an energy space so that it is a natural space in which to study the solutions note that p 2 is a special case for equation 2 indeed from the integrability theory see lax 14 we have for suitable u0 u0 and its derivatives with fast decay at infinity an infinite number of conservation laws the general question is to understand the dynamics induced by such equations local existence in time of solutions of 2 in the energy space is now well understood see kato 10 ginibre and tsutsumi 8 for the h theory s 32 kenig ponce and vega 11 for the l theory in the case of equation 1 and sharp h theory for 2 and bourgain 3 and 4 for the periodic case

bayesian model discrimination for multiple strata capture recapture data summary extending the work of dupuis 1995 we motivate a range of biologically plausible models for multiple site capture recapture and show how the original gibbs sampling algorithm of dupuis can be extended to obtain posterior model probabilities using reversible jump markov chain monte carlo this model selection procedure improves upon previous analyses in two distinct ways first bayesian model averaging provides a robust parameter estimation technique which properly incorporates model uncertainty in the resulting intervals secondly by discriminating among perhaps millions of competing models we are able to discern fine structure within the data and thereby answer questions of primary biological importance we demonstrate how reversible jump markov chain monte carlo methods provide the only viable method for exploring model spaces of this size we examine the lizard data discussed in dupuis 1995 and show that most of the posterior mass is placed upon models not previously considered for these data we discuss model discrimination and model averaging and focus upon the increased scientific understanding of the data obtained via the bayesian model comparison procedure

on inverse recursion operator and tri hamiltonian formulation for a kaup newell system of dnls equations an inverse of the recursion operator is computed and a clear presentation of a tri hamiltonian formulation is provided for a kaup newell system of derivative nonlinear schrodinger dnls equations therefore all kaup newell systems in the whole hierarchy of dnls equations are tri hamiltonian and have an inverse hierarchy of common commuting symmetries

global existence and blow up phenomena for the degasperis procesi equation this paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the degasperis procesi equation on the line global strong solutions to the equation are determined for a class of initial profiles on the other hand it is shown that the first blow up can occur only in the form of wave breaking a new wave breaking mechanism for solutions is described in detail and two results of blow up solutions with certain initial profiles are established

on the weak solutions to a shallow water equation we obtain the existence of global in time weak solutions to the cauchy problem for a one dimensional shallow water equation that is formally integrable and can be obtained by approximating directly the hamiltonian for euler s equation in the shallow water regime the solution is obtained as a limit of viscous approximation the key elements in our analysis are some new a priori one sided supernorm and space time higher norm estimates on the first order derivatives 2000 john wiley sons inc

an integrable semi discretization of the camassa holm equation and its determinant solution an integrable semi discretization of the camassa holm ch equation is presented the keys of its construction are bilinear forms and determinant structure of solutions of the ch equation determinant formulas of n soliton solutions of the continuous and semi discrete camassa holm equations are presented based on determinant formulas we can generate multi soliton multi cuspon and multi soliton cuspon solutions numerical computations using the integrable semi discrete camassa holm equation are performed it is shown that the integrable semi discrete camassa holm equation gives very accurate numerical results even in the cases of cuspon cuspon and soliton cuspon interactions the numerical computation for an initial value condition which is not an exact solution is also presented

on a camassa holm type equation with two dependent variables we consider a generalization of the camassa holm ch equation with two dependent variables called ch2 introduced in a paper by liu and zhang liu s q and zhang y 2005 j geom phys 54 427 53 we briefly provide an alternative derivation of it based on the theory of hamiltonian structures on the dual of a lie algebra the lie algebra involved here is the same algebra as underlies the nls hierarchy we study the structural properties of the hierarchy defined by the ch2 equation within the bi hamiltonian theory of integrable pdes and provide its lax representation then we explicitly discuss how to construct classes of solutions both of peakon and of algebro geometrical type finally we sketch the construction of a class of singular solutions defined by setting to zero one of the two dependent variables

stability of blow up profile and lower bounds for blow up rate for the critical generalized kdv equation the generalized korteweg de vries equations are a class of hamiltonian systems in infinite dimension derived from the kdv equation where the quadratic term is replaced by a higher order power term these equations have two conservation laws in the energy space h 1 l 2 norm and energy we consider in this paper the critical generalized kdv equation which corresponds to the smallest power of the nonlinearity such that the two conservation laws do not imply a bound in h 1 uniform in time for all h 1 solutions and thus global existence from 15 there do exist for this equation solutions u t such that u t h1 as t t where t we call them blow up solutions the question is to describe in a qualitative way how blow up occurs for solutions with l 2 mass close to the minimal mass allowing blow up and with decay in l 2 at the right we prove after rescaling and translation which leave invariant the l 2 norm that the solution converges to a universal profile locally in space at the blow up time t from the nature of this profile we improve the standard lower bound on the blow up rate for finite time blow up solutions

state space modeling of animal movement and mortality with application to salmon a stochastic model for the movement and eventual mortality of an individual animal is formulated as a combination of three components initial spatial location survival status at any point in time and spatial translation between points in time alternative theories about survival and migration can be expressed in terms of different models for any of the three components the model can be extended to groups of animals spatially and or temporally aggregated by appropriate integration when information about animal counts is partial or inexact as from mark recapture or harvest data state space models are a natural framework for estimating both unknown parameters and animal abundance as an example a multivariate linear normal state space model that explicitly incorporates each of the three individual animal components is formulated for the migration and harvest of pacific coho salmon oncorhynchus kisutch using recoveries of tagged coho salmon caught in ocean fisheries and associated measures of fishing effort the kalman filter and maximum likelihood are used to estimate parameters of the processes and the kalman smooth is used to estimate abundances given estimated parameters and current harvest and effort data real time management of exploited populations could be improved by using the kalman prediction algorithm

the trajectories of particles in stokes waves analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed within a period each particle experiences a backward forward motion with a slight forward drift

generalizations of the camassa holm equation we classify generalized camassa holm type equations which possess infinite hierarchies of higher symmetries we show that the obtained equations can be treated as negative flows of integrable quasi linear scalar evolution equations of orders 2 3 and 5 we present the corresponding lax representations or linearization transformations for these equations some of the obtained equations seem to be new

global weak solutions and blow up structure for the degasperis procesi equation in this paper we study several qualitative properties of the degasperis procesi equation we first established the precise blow up rate and then determine the blow up set of blow up strong solutions to this equation for a large class of initial data we finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions

lyapunov stability of ground states of nonlinear dispersive evolution equations on presente une nouvelle demonstration de la stabilite orbitale des solitons d etat fondamental de l equation de schrodinger non lineaire pour une grande classe de non linearites on demontre la stabilite de l onde solitaire pour l equation de korteweg de vries generalisee

the multiscale expansions of difference equations in the small lattice spacing regime and a vicinity and integrability test i we propose an algorithmic procedure i to study the distance between an integrable pde and any discretization of it in the small lattice spacing regime and at the same time ii to test the asymptotic integrability properties of such discretization this method should provide in particular useful and concrete information on how good is any numerical scheme used to integrate a given integrable pde the procedure illustrated on a fairly general ten parameter family of discretizations of the nonlinear schr dinger equation consists of the following three steps i the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in following degasperis et al 1997 physica d 100 187 211 ii the application to such an expansion of the degasperis procesi dp integrability test degasperis a and procesi m 1999 asymptotic integrability symmetry and perturbation theory spt98 ed a degasperis and g gaeta singapore world scientific pp 23 37 degasperis a 2001 multiscale expansion and integrability of dispersive wave equations lectures given at the euro summer school what is integrability isaac newton institute cambridge uk 13 24 august integrability lecture notes in physics vol 767 ed a mikhailov berlin springer to test the asymptotic integrability properties of the discrete system and its distance from its continuous limit iii the use of the main output of the dp test to construct infinitely many approximate symmetries and constants of motion of the discrete system through novel and simple formulas

blow up phenomena and local well posedness for a generalized camassa holm equation in the critical besov space abstract in this paper we mainly study the cauchy problem for a generalized camassa holm equation in a critical besov space first by using the littlewood paley decomposition transport equations theory logarithmic interpolation inequalities and osgood s lemma we establish the local well posedness for the cauchy problem of the equation in the critical besov space b 2 1 1 2 then we give a new blow up criterion for the cauchy problem of the equation finally we present a new blow up result and the exact blow up rate of strong solutions to the equation by making use of the conservation law and the obtained blow up criterion

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

finite propagation speed for the camassa holm equation we prove that any classical solution of the camassa holm equation will have compact support if its initial data has this property

traveling wave solutions of the degasperis procesi equation we classify all weak traveling wave solutions of the degasperis procesi equation in addition to smooth and peaked solutions the equation is shown to admit more exotic traveling waves such as cuspons stumpons and composite waves

self spreading and strength of singularities for solutions to semilinear wave equations algebres microlocales propagation de la regularite solutions lineaires conduisant a l etalement auto etalement des singularites

single and multi solitary wave solutions to a class of nonlinear evolution equations abstract in this paper an effective discrimination algorithm is presented to deal with equations arising from physical problems the aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations many examples are given to illustrate the algorithm at the same time some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations such as camassa holm equation kolmogorov petrovskii piskunov equation and so on then a direct constructive method called multi auxiliary equations expansion method is described to derive the multi solitary wave solutions of nonlinear evolution equations finally a class of novel multi solitary wave solutions of the 2 1 dimensional asymmetric version of the nizhnik novikov veselov equation are given by three direct methods the algorithm proposed in this paper can be steadily applied to some other nonlinear problems

global rough solutions to the critical generalized kdv equation abstract we prove that the initial value problem ivp for the critical generalized kdv equation u t u x x x u 5 x 0 on the real line is globally well posed in h s r if s 3 5 with the appropriate smallness assumption on the initial data

well posedness of a class of solutions to an integrable two component camassa holm system abstract in this paper we study a class of solutions to the cauchy problem for an integrable two component camassa holm system with the initial data u 0 0 1 h 1 r w 1 r l 2 r l r based on characteristics we study a corresponding ode and obtain a unique local solution by applying the contraction mapping principle we prove local existence and uniqueness of the solution to the camassa holm system by constructing a solution obtained from the ode and studying the regularity of the solution finally we show continuous dependence of the solution on the initial data in some weak sense