blow up and instability of solitary wave solutions to a generalized kadomtsev petviashvili equation in this paper we consider a generalized kadomtsev petviashvili equation in the form ut uxxx upux uyy x y e r2 t 0 it is shown that the solutions blow up in finite time for the supercritical power of nonlinearity p 4 3 with p the ratio of an even to an odd integer moreover it is shown that the solitary waves are strongly unstable if 2 p 4 that is the solutions blow up in finite time provided they start near an unstable solitary wave

uniqueness of non linear ground states for fractional laplacians in mathbb r we prove uniqueness of ground state solutions q q x 0 of the non linear equation sq q q 1 0inr s q q q 1 0 i n r where 0 s 1 and 0 4s 1 2s for s 12 s 1 2 and 0 for s 12 s 1 2 here s denotes the fractional laplacian in one dimension in particular we answer affirmatively an open question recently raised by kenig martel robbiano and we generalize by completely different techniques the specific uniqueness result obtained by amick and toland for s 12 s 1 2 and 1 in 5 for the benjamin ono equation as a technical key result in this paper we show that the associated linearized operator l s 1 1 q is non degenerate i e its kernel satisfies ker l span q this result about l proves a spectral assumption which plays a central role for the stability of solitary waves and blowup analysis for non linear dispersive pdes with fractional laplacians such as the generalized benjamin ono bo and benjamin bona mahony bbm water wave equations

optimal orlicz domains in sobolev embeddings into marcinkiewicz spaces abstract in this paper we present a method for determining whether there exists a largest orlicz space l a satisfying the sobolev embedding w m l a y where y stands for an arbitrary so called marcinkiewicz endpoint space the tool developed in this work enables us to investigate the optimality of orlicz domain spaces in sobolev embeddings and also in sobolev trace embeddings on domains in r n with various regularity

stability and instability of solitary waves of korteweg de vries type considered herein are the stability and instability properties of solitary wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear dispersive long waves special cases for which our analysis is decisive include equations of the korteweg de vries and benjamin ono type necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable

global well posedness for the kp i equation on the background of a non localized solution we prove that the cauchy problem for the kp i equation is globally well posed for initial data which are localized perturbations of arbitrary size of a non localized i e not decaying in all directions traveling wave solution e g the kdv line solitary wave or the zaitsev solitary waves which are localized in x and y periodic or conversely

fractional maximal operator in orlicz spaces abstract this work studies the fractional maximal operator acting between orlicz spaces the necessary and sufficient conditions for the existence of optimal target and domain spaces are established and the explicit formulas for corresponding optimal young functions are presented also we characterize whether the operator is bounded between two given orlicz spaces

optimal sobolev imbeddings involving rearrangement invariant quasinorms let m and n be positive integers with n 2 and 1 m n 1 we study rearrangement invariant quasinorms r and d on functions f 0 1 view the mathml source such that to each bounded domain in view the mathml sourcen with lebesgue measure there corresponds c c 0 for which one has the sobolev imbedding inequality r u t c d mu t u cm0 involving the nonincreasing rearrangements of u and a certain mth order gradient of u when m 1 we deal in fact with a closely related imbedding inequality of talenti in which d need not be rearrangement invariant r u t c d d dt x view the mathml sourcen u x u t u x dx u c10 in both cases we are especially interested in when the quasinorms are optimal in the sense that r cannot be replaced by an essentially larger quasinorm and d cannot be replaced by an essentially smaller one our results yield best possible refinements of such limiting sobolev inequalities as those of trudinger strichartz hansson brezis and wainger

quasilinear elliptic equations on noncompact riemannian manifolds abstract the existence of solutions to a class of quasilinear elliptic problems on noncompact riemannian manifolds with finite volume is investigated boundary value problems with homogeneous neumann conditions in possibly irregular euclidean domains are included as a special instance a nontrivial solution is shown to exist under an unconventional growth condition on the right hand side which depends on the geometry of the underlying manifold the identification of the critical growth is a crucial step in our analysis and entails the use of the isocapacitary function of the manifold a condition involving its isoperimetric function is also provided

rational solutions of the kadomtsev petviashvili hierarchy and the dynamics of their poles i new form of a general rational solution a new approach to the construction of the rational solutions to the hierarchy of the kadomtsev petviashvili equation is presented the generalization of the superposition formula is found to permit the construction of a new general solution from some partial ones the features of the general polynomial factorization and the types of scattering in the many body calogero moser problem are investigated

stability of the line soliton of the kp ii equation under periodic transverse perturbations we prove the nonlinear stability of the kdv solitary waves considered as solutions of the kp ii equation with respect to periodic transverse perturbations our proof uses a miura transform which sends the solutions of an mkp ii equation to solutions of the kp ii equation

rational solutions of integrable equations via nonlinear superposition formulae in this paper a method is developed to obtain rational solutions of integrable equations which include kdv boussinesq kp ito 1 1 dimensional cdgks ramani and 2 1 dimensional cdgks equations the key step that we use to find rational solutions of these equations is the use of nonlinear superposition formulae all these rational solutions obtained for each equation are connected by a backlund transformation which enables us to find other new solutions through the nonlinear superposition of rational solutions and other known solutions

a particle swarm optimization for solving joint pricing and lot sizing problem with fluctuating demand and unit purchasing cost in this paper we extend the classical economic order quantity model to allow for not only a function of price dependent and time varying demand but also fluctuating unit purchasing cost the joint replenishment problem is subject to continuous decay and a general partial backlogging rate the objective is to find the optimal replenishment number time scheduling and periodic selling price to maximize the discounted total profit an effective search procedure is provided to find the optimal solution by employing the properties derived in this paper and particle swarm optimization algorithm several numerical examples are used to illustrate the features of the proposed model

optimal sobolev trace embeddings optimal target spaces are exhibited in arbitrary order sobolev type embeddings for traces of n dimensional functions on lower dimensional subspaces sobolev spaces built upon any rearrangement invariant norm are allowed a key step in our approach consists in showing that any trace embedding can be reduced to a one dimensional inequality for a hardy type operator depending only on n and on the dimension of the relevant subspace this can be regarded as an analogue for trace embeddings of a well known symmetrization principle for first order sobolev embeddings for compactly supported functions the stability of the optimal target space under iterations of sobolev trace embeddings is also established and is part of the proof of our reduction principle as a consequence we derive new trace embeddings with improved optimal target spaces for classical sobolev lorentz sobolev and orlicz sobolev spaces

price determination for an eoq model for deteriorating items under perfect competition the problem of price determination for an eoq model under perfect competition is of central importance in the field of inventory control and management especially for such kind of models which study the dynamics of the market economy over time in this paper an attempt has been made to analyze and compute the price of a unit item of inventory for an eoq model for deteriorating items under the perfect competition as an important market structure along with the optimization technique the marginal revenue and marginal cost approach has been employed to determine the price of a unit item of inventory the present work is presumably believed to provide theoretical as well as applicable insight for marketing experts and inventory managers engaged in this field

optimal gaussian sobolev embeddings abstract a reduction theorem is established showing that any sobolev inequality involving arbitrary rearrangement invariant norms with respect to the gauss measure in r n is equivalent to a one dimensional inequality for a suitable hardy type operator involving the same norms with respect to the standard lebesgue measure on the unit interval this result is exploited to provide a general characterization of optimal range and domain norms in gaussian sobolev inequalities applications to special instances yield optimal gaussian sobolev inequalities in orlicz and lorentz zygmund spaces point out new phenomena such as the existence of self optimal spaces and provide further insight into classical results

decay mode solution of the two dimensional kdv equation and the generalized backlund transformation we consider the generalization of the customary backlund transform bt for the two dimensional 2d kdv equation ut 6uux uxxx x 3 2uyy 0 with being constant a nonlinear superposition formula has been obtained and it is shown that the present generalized bt can produce multiple soliton multiple decay mode solutions

stability and instability of the kdv solitary wave under the kp i flow we consider the kp i and gkp i equations in mathbb r times mathbb r 2 pi mathbb z we prove that the kdv soliton with subcritical speed 0 c in the spirit of the work by duyckaerts and merle gafa 18 1787 1840 2009 we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity this last result also holds for the gkp i equation

a numerical approach to a multi objective optimal inventory control problem for deteriorating multi items under fuzzy inflation and discounting the optimal production and advertising policies for an inventory control system of deteriorating multi items under a single management are formulated with resource constraints under inflation and discounting in fuzzy environment here the deterioration of the items and depreciation of sales are at a constant rate deteriorated items are salvaged and the effect of inflation and time value of money are taken into consideration the inflation and discount rates are assumed to be imprecise and represented by fuzzy numbers these imprecise quantities are first transformed to corresponding intervals and then following interval mathematics the related objective function is changed to respective multi objective functions using utility function method ufm the multi objective problem is changed to a single objective problem here the production and advertisement rates are unknown and considered as control decision variables the production advertisement and demand rates are functions of time t the total profit which consists of the sales proceeds production cost inventory holding cost and advertisement cost is formulated as an optimal control problem and evaluated numerically using ufm and generalized reduced gradient grg technique finally numerical experiment sensitivity analysis and graphical representation are provided to illustrate the system for the present model expressions and graphical results are presented when the rates of advertisement are constant

higher order sobolev embeddings and isoperimetric inequalities abstract optimal higher order sobolev type embeddings are shown to follow via isoperimetric inequalities this establishes a higher order analogue of a well known link between first order sobolev embeddings and isoperimetric inequalities sobolev type inequalities of any order involving arbitrary rearrangement invariant norms on open sets in r n possibly endowed with a measure density are reduced to much simpler one dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets as a consequence the optimal target space in the relevant sobolev embeddings can be determined both in standard and in non standard classes of function spaces and underlying measure spaces in particular our results are applied to any order sobolev embeddings in regular john domains of the euclidean space in maz ya classes of possibly irregular euclidean domains described in terms of their isoperimetric function and in families of product probability spaces of which the gauss space is a classical instance

phase dynamics of periodic waves leading to the kadomtsev petviashvili equation in 3 1 dimensions the kadomstev petviashvili kp equation is a well known modulation equation normally derived by starting with the trivial state and an appropriate dispersion relation in this paper it is shown that the kp equation is also the relevant modulation equation for bifurcation from periodic travelling waves when the wave action flux has a critical point moreover the emergent kp equation arises in a universal form with the coefficients determined by the components of the conservatio n of wave action the theory is derived for a general class of partial differential equations generated by a lagrangian using phase modulation the theory extends to any space dimension and time but the emphasis in the paper is on the ca se of 3 1 motivated by light bullets and quantum vortex dynamics the theory is illustrated by showing how defocussing nls in 3 1 bifurcates to kp in 3 1 at criticality the generalization to n 3 is also discussed

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

rational solutions of the kp hierarchy and the dynamics of their poles ii construction of the degenerate polynomial solutions a general approach to constructing the polynomial solutions satisfying various reductions of the kadomtsev petviashvili kp hierarchy is described within this approach the reductions of the kp hierarchy are equivalent to certain differential equations imposed on the function of the hierarchy in particular the l reduction and the k constraint as well as their generalized counterparts are considered a general construction of the rational solutions to these reductions is found and the particular solutions are explicitly derived for some typical examples including the kdv and gardner equations the boussinesq and classical boussinesq systems the nls and yajima oikawa equations it is shown that the degenerate rational solutions of the kp hierarchy are related to stationary manifolds of the calogero moser cm hierarchy of dynamical systems the scattering dynamics of interacting particles in the cm systems may become complicated due to an anomalously slow fractional power rate of the particle motion along the stationary manifolds

on the discrete spectrum of the nonstationary schrodinger equation and multipole lumps of the kadomtsev petviashvili i equation the discrete spectrum of the nonstationary schrodinger equation and localized solutions of the kadomtsev petviashvili i kpi equation are studied via the inverse scattering transform it is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter an index or winding number is asssociated with each of these solutions the resulting localized solutions of kpi behave as collection of individual humps with nonuniform dynamics

optimal replenishment policies with allowable shortages for a product life cycle in this paper we investigate replenishment policies with allowable shortages by considering a general time varying continuous and deterministic demand function for a product life cycle the objective is to optimally determine the number of inventory replenishments the inventory replenishment time points and the beginning time points of shortages within the product life cycle by minimizing the total relevant costs of the inventory replenishment system the proposed problem is mathematically formulated as a mixed integer nonlinear programming model a complete search procedure is developed to find the optimal solution by employing the properties derived in this paper and the well known nelder mead algorithm also several numerical examples and the corresponding sensitivity analyses are carried out to illustrate the features of our model by utilizing the search procedure developed in this paper

a new algorithm for optimally determining lot sizing policies for a deteriorating item in an integrated production inventory system in this study we focus on optimally determining lot sizing policies for a deteriorating item among all the partners in a supply chain system with a single vendor and multiple buyers so as to minimize the average total costs we revise yang and wee s 1 model using the fourier series to precisely estimate the vendor s inventory holding costs also we transform our revised model into a more concise version by applying anapproximation to the exponential terms in the objective function in order to solve this problem we analyze the optimality structure of our revised model and derive several interesting properties by utilizing our theoretical results we propose a search algorithm that can efficiently solve the optimal solution based on our numerical experiments we show that the proposed algorithm outperforms the existing solution approach in the literature especially when the number of buyers is larger in the supply chain system

orlicz sobolev boundary trace embeddings we prove a sharp trace embedding theorem for orlicz sobolev spaces into orlicz spaces on the boundary an optimal trace embedding into more general rearrangement invariant spaces on the boundary is also established

wave collapse and instability of solitary waves of a generalized kadomtsev petviashvili equation abstract the solutions of a family of generalized kadomtsev petviasvili equation in two diemnsions u t u m u x u xxx x 2 u yy are studied with appropriate boundary conditions and constraints on the initial data for m in a dense set m 0 and for 2 1 if m 4 then the solution can blow up in finite time we show that if 1 m 4 a solitary wave so exists which is unstable if m 4 3 in this and related problems th e instability of solitary waves is associated with onset of wave collapse we give numerical evidence to support this

nondegeneracy morse index and orbital stability of the kp i lump solution using backlund transformation we analyze the spectral property of the kp i lump solution it is proved that the lump is nondegenerate and its morse index equals one as a consequence we show that it is orbitally stable

asymptotic stability of n solitary waves of the fpu lattices we study stability of n solitary wave solutions of the fermi pasta ulam fpu lattice equation solitary wave solutions of the fpu lattice equation cannot be characterized as critical points of conservation laws due to the lack of infinitesimal invariance in the spatial variable in place of standard variational arguments for hamiltonian systems we use an exponential stability property of the linearized fpu equation in a weighted space which is biased in the direction of motion the dispersion of the linearized fpu equation balances the potential term for low frequencies whereas the dispersion is superior for high frequencies we approximate the low frequency part of a solution of the linearized fpu equation by a solution to the linearized korteweg de vries kdv equation around an n soliton solution we prove an exponential stability property of the linearized kdv equation around n solitons by using the linearized backlund transformation and use the result to analyze the linearized fpu equation

a possibilistic multiple objective pricing and lot sizing model with multiple demand classes we address an inventory marketing system to determine the production lot size marketing expenditure and selling prices where a firm faces demand from two or more market segments in which the firm can set different prices considering pricing marketing and lot sizing decisions simultaneously the model maximizes the profit and return on inventory investment under multiple time varying demand classes the model is formulated as a fuzzy non linear multi objective one where some parameters are ill known and modeled by fuzzy numbers a hybrid possibilistic flexible programming approach is proposed to handle imprecise data and soft constraints concurrently after transforming the original model into an equivalent multi objective crisp model it is then converted to a classical mono objective one by a fuzzy goal programming method an efficient solution procedure using particle swarm optimization pso is also provided to solve the resulting non linear problem

rarefaction pulses for the nonlinear schrodinger equation in the transonic limit we investigate the properties of finite energy travelling waves to the nonlinear schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities in space dimension two and three we prove that travelling waves converge in the transonic limit up to rescaling to ground states of the kadomtsev petviashvili equation our results generalize an earlier result of f bethuel p gravejat and j c saut for the two dimensional gross pitaevskii equation and provide a rigorous proof to a conjecture by c jones and p h roberts about the existence of an upper branch of travelling waves in dimension three