non perturbative solution of the klein gordon zakharov equation abstract the initial value problem for the klein gordon zakharov equation is solved by decomposition for x r 3

instability of standing waves for klein gordon zakharov equations with different propagation speeds in three space dimensions abstract this paper is concerned with the standing wave for klein gordon zakharov equations with different propagation speeds in three space dimensions the existence of standing wave with the ground state is established by applying an intricate variational argument and the instability of the standing wave is shown by applying pagne and sattinger s potential well argument and levine s concavity method

new results on the synthesis of pid controllers this paper considers the problem of stabilizing a first order plant with dead time using a proportional integral derivative pid controller using a version of the hermite biehler theorem that is applicable to quasi polynomials the complete set of stabilizing pid parameters is determined for both open loop stable and unstable plants the range of admissible proportional gains is first determined in closed form for each proportional gain in this range the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid a triangle or a quadrilateral for the case of an open loop unstable plant a necessary and sufficient condition on the time delay is determined for the existence of stabilizing pid controllers

normal forms and quadratic nonlinear klein gordon equations on construit une transformation qui change l equation a non linearite cubique que l on sait resoudre a 3 1 dimensions on demontre que la solution du probleme original a le meme comportement asymptotique que l equation de klein gordon non lineaire

interaction equations for short and long dispersive waves abstract we show the time local well posedness for a system of nonlinear dispersive equations for the water wave interaction formula it is shown that for any initial data u0 v0 hs r hs 1 2 r s 0 the solution for the above equation uniquely exists in a subset ofc t t hs c t t hs 1 2 and depends continuously on the data by virtue of a special structure of the nonlinear coupling the solution is stable under a singular limiting process

stability of semiclassical bound states of nonlinear schrodinger equations with potentials in this paper we study the lyapunov stabilities of some semiclassical bound states of the nonhomogeneous nonlinear schrodinger equation we prove that among those bound states those which are concentrated near local minima respectively maxima of the potentialv are stable respectively unstable we also prove that those bound states are positive if is sufficiently small

convergence of an efficient and compact finite difference scheme for the klein gordon zakharov equation a compact and semi explicit finite difference scheme is proposed and analyzed for the klein gordon zakharov kgz equation the new scheme is decoupled and linearized in practical computation i e at each time step only two tri diagonal systems of linear algebraic equations need to be solved by thomas algorithm so the new scheme is more efficient and more accurate than the classical finite difference schemes unique solvability of the difference solution is proved by using the energy method besides the standard energy method in order to overcome the difficulty in obtaining the a priori estimate an induction argument is introduced to prove that the new scheme is convergent for u x t in the discrete h 1 norm and respectively for m x t in the discrete l 2 norm at the order of o 2 h 4 with time step and mesh size h numerical results are reported to verify the theoretical analysis

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

nonlinear small data scattering for the wave and klein gordon equation on etudie l operateur diffusion qui appartient a la paire d equations u tt au f u 0 et u tt au 0 a represente l operateur j 1 n 2 x j 2 m 2 m r et f u u 1 u ou r 1

numerical solutions of coupled kleingordonzakharov equations by quintic b spline differential quadrature method numerical solutions of the coupled kleingordonzakharov equations are obtained by using quintic b spline based differential quadrature method a rungekutta fourth method is used for time integration stability of the scheme is studied using matrix stability analysis the accuracy and efficiency of the presented method is shown by conducting some numerical experiments on test problems which includes the motion of single soliton and interactions of two solitons the numerical results are found in good agreement with the exact solutions

a system to measure the kinematics during the entire ski jump sequence using inertial sensors three dimensional analysis of the entire sequence in ski jumping is recommended when studying the kinematics or evaluating performance camera based systems which allow three dimensional kinematics measurement are complex to set up and require extensive post processing usually limiting ski jumping analyses to small numbers of jumps in this study a simple method using a wearable inertial sensors based system is described to measure the orientation of the lower body segments sacrum thighs shanks and skis during the entire jump sequence this new method combines the fusion of inertial signals and biomechanical constraints of ski jumping its performance was evaluated in terms of validity and sensitivity to different performances based on 22 athletes monitored during daily training the validity of the method was assessed by comparing the inclination of the ski and the slope at landing point and reported an error of 0 2 4 8 the validity was also assessed by comparison of characteristic angles obtained with the proposed system and reference values in the literature the differences were smaller than 6 for 75 of the angles and smaller than 15 for 90 of the angles the sensitivity to different performances was evaluated by comparing the angles between two groups of athletes with different jump lengths and by assessing the association between angles and jump lengths the differences of technique observed between athletes and the associations with jumps length agreed with the literature in conclusion these results suggest that this system is a promising tool for a generalization of three dimensional kinematics analysis in ski jumping

on almost global existence for nonrelativistic wave equations in 3d almost global solutions are constructed to three dimensional quadratically nonlinear wave equations the proof relies on generalized energy estimates and a new decay estimate the method applies to equations that are only classically invariant such as the nonlinear system of hyperelasticity 1996 john wiley sons inc

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

fourier analysis of trunk displacements a method to identify the lame limb in trotting horses the aim of this paper is to present a method allowing the identification of the lame limb in trotting horses using a 3 d kinematic analysis system 13 sound and 25 lame horses fitted with 4 skin markers placed on the dorsal midline of their trunk were recorded while trotting on a track in the conditions of the routine lameness examination the vertical displacements of the trunk markers underwent fourier analysis results indicated that these displacements could be represented using only the first and second harmonics from these two harmonics indices were then developed the sensitivity of these indices to the different types of experimental errors was also studied results showed that the values of the indices of the lame horses were relatively unaffected by the experimental errors in lame horses these indices allowed the quantification of the degree of the lameness the identification of lame limb with a reliability 95 and the characterisation of the type of trunk movements these indices could be easily implemented in a computer program to provide objective information to the clinician or to be used as a first step in the development of an expert system moreover these clinical tools may also be extended to other quadrupedal or bipedal locomotions r 2002 elsevier science ltd all rights reserved

on the stabilizing pid controllers for integral processes in this note we show how to determine the set of stabilizing parameters of a proportional integral derivative controller for an integrator plus dead time process in particular by exploiting a version of the hermite biehler theorem applicable to quasipolynomals the admissible range of the proportional gain is computed first then for each value of the proportional gain in that range the set of stabilizing values of the integral and derivative gain are found it is shown that the procedure is greatly simplified with respect to the case of a second order integral process with dead time

identifying gait asymmetry using gyroscopes a cross correlation and normalized symmetry index approach abstract injury to a lower limb may disrupt natural walking and cause asymmetrical gait therefore assessing the gait asymmetry has become one of the important procedures in gait analysis this paper proposes the use of wireless gyroscopes as a new instrument to determine gait asymmetry it also introduces two novel approaches normalized cross correlations cc norm and normalized symmetry index si norm cc norm evaluates the waveform patterns generated by the lower limb in each gait cycle si norm provides indications on the timing and magnitude of the bilateral differences between the limbs while addressing the drawbacks of the conventional methods one way anova test reveals that cc norm can be considered as single value indicator that determines the gait asymmetry p si norm in asymmetrical gait were different from normal gait si norm in asymmetrical gait were found to be approximately 20 greater than si norm in normal gait during pre swing and initial swing

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

new exact traveling wave solutions for the klein gordon zakharov equations based on the extended hyperbolic functions method we obtain the multiple exact explicit solutions of the klein gordon zakharov equations the solutions obtained in this paper include a the solitary wave solutions of bell type for u and n b the solitary wave solutions of kink type for u and bell type for n c the solitary wave solutions of a compound of the bell type and the kink type for u and n d the singular traveling wave solutions e periodic traveling wave solutions of triangle function types and solitary wave solutions of rational function types we not only rederive all known solutions of the klein gordon zakharov equations in a systematic way but also obtain several entirely new and more general solutions the variety of structures of the exact solutions of the klein gordon zakharov equations is illustrated

a uniformly accurate multiscale time integrator spectral method for the kleingordonzakharov system in the high plasma frequency limit regime a multiscale time integrator sine pseudospectral mti sp method is presented for discretizing the kleingordonzakharov kgz system with a dimensionless parameter 0 1 which is inversely proportional to the plasma frequency in the high plasma frequency limit regime i e 0 1 the solution of the kgz system propagates waves with amplitude at o 1 and wavelength at o 2 in time and o 1 in space which causes significantly numerical burdens due to the high oscillation in time the main idea of the numerical method is to carry out a multiscale decomposition by frequency mdf to the electric field component of the solution at each time step and then apply the sine pseudospectral discretization for spatial derivatives followed by using the exponential wave integrator in phase space for integrating the mdf and the equation of the ion density component the method is explicit and easy to be implemented extensive numerical results show that the mti sp method converges uniformly and optimally in space with exponential convergence rate if the solution is smooth and uniformly in time with linear convergence rate at o for 0 1 with time step size and optimally with quadratic convergence rate at o 2 in the regime when either o 1 or 0 thus the meshing strategy requirement or scalability of the mti sp for the kgz system in the high plasma frequency limit regime is o 1 and h o 1 for 0 1 which is significantly better than classical methods in the literatures finally we apply the mti sp method to study the convergence rates of the kgz system to its limiting models in the high plasma frequency limit and the interactions of bright solitons of the kgz system and to identify certain parameter regimes that the solution of the kgz system will be blow up in one dimension

instability of nonlinear bound states we establish a sharp instability theorem for the bound states of lowest energy of the nonlinear klein gordon equation utt u f u 0 and the nonlinear schrodinger equation iut u f u 0

counterexamples to local existence for semi linear wave equations in this paper we study how much regularity of initial data is needed to ensure existence of a local solution to a semi linear wave equation we give counterexamples to local existence for the typical model equations the counterexamples we construct are sharp i e one does have a local solution if the data has slightly more regularity

advanced resource connector middleware for lightweight computational grids as computational grids move away from the prototyping state reliability performance and ease of use and maintenance become focus areas of their adoption in this paper we describe arc advanced resource connector grid middleware where these issues have been given special consideration we present an in depth view of the existing components of arc and discuss some of the new components functionalities and enhancements currently under development this paper also describes architectural and technical choices that have been made to ensure scalability stability and high performance the core components of arc have already been thoroughly tested in demanding production environments where it has been in use since 2002 the main goal of this paper is to provide a first comprehensive description of arc

comments on new results on the synthesis of pid controllers silva datta and bhattacharyya in the above paper have studied the feedback control system provided with a proportional integral derivative pid controller and relative to a first order plant with a time delay and have determined the range of the pid controller parameters suitable for the stability by means of a version of the hermite biehler theorem the purpose of this note is to find the same results in a simpler way by means of the classical nyquist s stability criterion

on potential wells and applications to semilinear hyperbolic equations and parabolic equations abstract in this paper we generalize the family of potential wells to the initial boundary value problem of semilinear hyperbolic equations and parabolic equations u tt u f u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 and u t u f u x t 0 u x 0 u 0 x x u x t 0 x t 0 not only give a threshold result of global existence and nonexistence of solutions but also obtain the vacuum isolating of solutions finally we prove the global existence of solutions for above problem with critical initial conditions i u 0 0 e 0 d or i u 0 0 j u 0 d so payne and sattinger s results are generalized and improved in essential

technical communique stability of pid controlled second order time delay feedback systems in the previous papers the stability of pid controlled first order time delay systems has been investigated by means of several methods of which the nyquist criterion a generalization of the hermite biehler theorem and the root location method are well known explicit expressions of the boundaries of the stability region which is the set of controller parameters that give stable closed loop systems have been determined from these studies one can verify that not all plants can be made stable and then obtain the set of process parameters that allow stable closed loop systems with this set one can implement the stability region of the process parameters in a recent paper the stability conditions based on pontryagin s studies and valid for arbitrary order plants have been presented the procedure deduced for the controller parameters is exhaustive but that deduced for the process parameters requires further mathematical evaluations whose complexity is proportional to the number of process time constants in the aforementioned recent paper these evaluations have been performed for a second order time delay plant whose transfer function has no zero the aim of this paper is to execute these calculations for a second order plant whose transfer function has one zero and to provide the related stability region

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

on the cauchy problem for the zakharov system abstract we study the local cauchy problem in time for the zakharov system 1 1 and 1 2 governing langmuir turbulence with initial data u 0 n 0 t n 0 h k h lscr h l 1 in arbitrary space dimension we define a natural notion of criticality according to which the critical values of k l are 2 3 2 2 2 using a method recently developed by bourgain we prove that the zakharov system is locally well posed for a variety of values of k l the results cover the whole subcritical range for 4 for 3 they cover only part of it and the lowest admissible values are k l 1 2 0 for 2 3 and k l 0 1 2 for 1 as a by product of the one dimensional result we prove well posedness of the benney system 1 14 and 1 15 governing the interaction of short and long waves for the same values of k l

instability of standing wave global existence and blowup for the klein gordon zakharov system with different degree nonlinearities abstract this paper discusses the klein gordon zakharov system with different degree nonlinearities in two and three space dimensions firstly we prove the existence of standing wave with ground state by applying an intricate variational argument next by introducing an auxiliary functional and an equivalent minimization problem we obtain two invariant manifolds under the solution flow generated by the cauchy problem to the aforementioned klein gordon zakharov system furthermore by constructing a type of constrained variational problem utilizing the above two invariant manifolds as well as applying potential well argument and concavity method we derive a sharp threshold for global existence and blowup then combining the above results we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation finally we prove a modified instability of standing wave to the system under study

ambulatory measurement of 3d knee joint angle three dimensional measurement of joint motion is a promising tool for clinical evaluation and therapeutic treatment comparisons although many devices exist for joints kinematics assessment there is a need for a system that could be used in routine practice such a system should be accurate ambulatory and easy to use the combination of gyroscopes and accelerometers i e inertial measurement unit has proven to be suitable for unrestrained measurement of orientation during a short period of time i e few minutes however due to their inability to detect horizontal reference inertial based systems generally fail to measure differential orientation a prerequisite for computing the three dimentional knee joint angle recommended by the internal society of biomechanics isb a simple method based on a leg movement is proposed here to align two inertial measurement units fixed on the thigh and shank segments based on the combination of the former alignment and a fusion algorithm the three dimensional knee joint angle is measured and compared with a magnetic motion capture system during walking the proposed system is suitable to measure the absolute knee flexion extension and abduction adduction angles with mean sd offset errors of 1 degree 1 degree and 0 degrees 0 6 degrees and mean sd root mean square rms errors of 1 5 degrees 0 4 degrees and 1 7 degrees 0 5 degrees the system is also suitable for the relative measurement of knee internal external rotation mean sd offset error of 3 4 degrees 2 7 degrees with a mean sd rms error of 1 6 degrees 0 5 degrees the method described in this paper can be easily adapted in order to measure other joint angular displacements such as elbow or ankle

reliable computation of pid gain space for general second order time delay systems abstractthis paper addresses the problem of determining the stability gain space of a pid controller for general second order time delay systems first a review of existing results and the associated drawbacks is presented subsequently a new algorithm to compute the entire pid stability gain space is developed the new algorithm is based upon existing results on the relationship between the stability of a quasi polynomial and its derivatives an extended version of the hermit biehler theorem and also the nyquist criterion the algorithm entails extraction of an admissible range for the pid parameter kp and then based on this range a stability region in the ki kd plane is computed well known examples are studied to demonstrate the reliability and accuracy of the results

extended wave solutions for a nonlinear klein gordon zakharov system abstract the nonlinear klein gordon zakharov kgz system is used as a vehicle to employ the sine cosine method and the extended tanh method to construct formally exact wave solutions each method presents various solutions with distinct formal properties and physical structures which mainly include new periodic wave solutions traveling wave solutions and solitary solutions in addition as special cases some of new rational functions type solutions are developed and extended

an exponential wave integrator sine pseudospectral method for the klein gordon zakharov system an exponential wave integrator sine pseudospectral method is presented and analyzed for discretizing the klein gordon zakharov kgz system with two dimensionless parameters 0 varepsilon le 1 and 0 gamma le 1 which are inversely proportional to the plasma frequency and the speed of sound respectively the main idea in the numerical method is to apply the sine pseudospectral discretization for spatial derivatives followed by using an exponential wave integrator for temporal derivatives in phase space the method is explicit symmetric in time and it is of spectral accuracy in space and second order accuracy in time for any fixed varepsilon varepsilon 0 and gamma gamma 0 in the mathcal o 1 plasma frequency and speed of sound regime i e varepsilon mathcal o 1 and gamma mathcal o 1 we establish rigorously error estimates for the numerical method in the energy space h 1 times l 2 we also study numerically the resolution of the method in the simultaneous high plasma fr

symmetry indices based on accelerometric data in trotting horses detection and quantification of lameness in horses consists primarily of a subjective assessment whereby both intra and inter observer disagreements exist especially with low grade lameness therefore clinically applicable methods are needed for reliable objective assessments the aim of this study was to describe three symmetry indices derived from a simple accelerometric method and investigate these in sound trotting horses the indices describe the overall symmetry of the gait the symmetry of loads placed on the limbs and the symmetry in timing between left and right steps these symmetry indices were able to quantify the high degree of symmetry of the trot in sound horses that has been described in earlier studies using other gait analysis methods also we have analysed the variances and have found high repeatability for all three indices this provides a basis for future investigations of the symmetry indices and their potential for objective detection and quantification of lameness in horses

a perturbative analysis of the time envelope approximation in strong langmuir turbulence abstract we investigate a nonlinear set of coupled wave equations describing the inertial regime of the strong langmuir turbulence 1 2 2 e t 2 2i e t e ne 1 c 2 2 n t 2 n e 2 which differs from the usual zakharov equations by the inclusion in the first equation for e of a second time derivative multiplied by the parameter 1 2 that vanishes under the so called time envelope approximation 2 a from these perturbed zakharov equations it is shown that the latter limit is not compatible with a strongly dominant ion inertia corresponding to the formal case c 2 a 0 in the opposite case i e as c2 remains of order unity the local in time cauchy problem attached to the above equations is solved and the limit 2 a is detailed for a fixed value of c2 under some specific initial data the solution e is proved to blow up at least in an infinite time provided that lies below a threshold value when this condition is not fulfilled the global existence of the solution set e n is finally restored in a one dimensional space

fourth order wave equations with nonlinear strain and source terms abstract in this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms first we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions then we obtain a threshold result of global existence and nonexistence finally we discuss the global existence of solutions for the problem with critical initial condition i u 0 0 e 0 d so the esquivel avila s results are generalized and improved

further results on the synthesis of pid controllers this note focuses on a graphical approach to determine the stability region in the parameter space of pid controlled second order plants with dead time this work is the extension of and further results on the same topic of the previous paper in the literature on first order plants with dead time the main characterization of the new method is the utilization of a graphical stability criterion in the parameter space which releases a necessary and sufficient stability condition once the range of proportional gain is known the complete stabilizing set in the plain of integral derivative gains can be drawn and identified immediately not to be computed mathematically a practical algorithm of drawing the stabilizing boundaries in the integral derivative space is proposed

a uniformly and optimally accurate multiscale time integrator method for the klein gordon zakharov system in the subsonic limit regime abstract we present a uniformly and optimally accurate numerical method for discretizing the klein gordon zakharov system kgz with a dimensionless parameter 0 e 1 which is inversely proportional to the acoustic speed in the subsonic limit regime i e 0 e 1 the solution of kgz system propagates waves with o e and o 1 wavelength in time and space respectively and rapid outspreading initial layers with speed o 1 e in space due to the singular perturbation of the wave operator in kgz and or the incompatibility of the initial data based on a multiscale decomposition by frequency and amplitude we propose a multiscale time integrator fourier pseudospectral method by applying the fourier spectral discretization for spatial derivatives followed by using the exponential wave integrator in phase space for integrating the decomposed system at each time step the method is explicit and easy to be implemented extensive numerical results show that the mti fp method converges optimally in both space and time with exponential and quadratic convergence rate respectively which is uniformly for e 0 1 finally the method is applied to study the convergence rates of the kgz system to its limiting models in the subsonic limit and wave dynamics and interactions of the kgz system in 2d

potential well method for cauchy problem of generalized double dispersion equations abstract in this paper we study cauchy problem of generalized double dispersion equations u t t u x x u x x t t u x x x x f u x x where f u u p p 1 or u 2 k k 1 2 by introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions but also obtain the invariance of some sets and vacuum isolating of solutions in addition the global existence and finite time blow up of solutions for problem with critical initial conditions e 0 d i u 0 0 or i u 0 0 are proved

arbitrary precision computation of the set of stabilising gains for time delay lti systems a new method is proposed to calculate the set of proportional controllers stabilising a given linear time invariant system with a fixed time delay the method is based on the utilisation of pade approximations for the time delay lam s studies on the convergence of pade approximations and a generalisation of the nyquist theorem applicable to quasi polynomials the method allows determination of the closeness of the resulting set to the exact set of stabilising gains by tracing the uncertainty introduced by the pade approximation as a result it is possible to approximate the resulting set arbitrarily close to the exact stabilising set

on the bound states of the nonlinear schrodinger equation with a linear potential abstract we study the nonlinear schrodinger equation with an attractive linear potential i t v x 2 0 n 2 nls which arises in the mathematical description of phenomena in nonlinear optics and plasma physics nonlinear bound states are finite energy localized solutions which if dynamically stable play an important role in the structure of general solutions of nls we discuss the existence and nonlinear orbital stability of nonlinear ground states of nls in particular if v supports a linear bound state then nls has stable nonlinear ground states in the supercritical and critical cases 2 n where blow up self focusing or collapse can occur this is a phenomenon not present in the case where v 0 in addition islands of stability in the regime of large h1 norm exist

energy convergence for singular limits of zakharov type systems we prove existence and uniqueness of solutions to the klein gordon zakharov system in the energy space h1 l2 on some time interval which is uniform with respect to two large parameters c and these two parameters correspond to the plasma frequency and the sound speed in the simultaneous high frequency and subsonic limit we recover the nonlinear schrodinger system at the limit we are also able to say more when we take the limits separately

galerkin finite element methods for the generalized klein gordon zakharov equations abstract in this paper we propose galerkin finite element methods to investigate the evolution of the generalized klein gordon zakharov equations the spatial discretization is based on galerkin finite element method the combination of time splitting method and finite difference method is used for temporal discretization the accuracy and efficiency of our numerical schemes are verified by the error norms conservation laws and the application in nonrelativistic limit regime and in three spatial dimension of different numerical experiments

a class of fourth order wave equations with dissipative and nonlinear strain terms we study the initial boundary value problem for a class of fourth order wave equations with dissipative and nonlinear strain terms by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence and nonexistence of solutions

accuracy and precision of hind limb foot contact timings of horses determined using a pelvis mounted inertial measurement unit abstract gait analysis using small sensor units is becoming increasingly popular in the clinical context in order to segment continuous movement from a defined point of the stride cycle knowledge about footfall timings is essential we evaluated the accuracy and precision of foot contact timings of a defined limb determined using an inertial sensor mounted on the pelvis of ten horses during walk and trot at different speeds and in different directions foot contact was estimated from vertical velocity events occurring before maximum sensor roll towards the contralateral limb foot contact timings matched data from a synchronised hoof mounted accelerometer well when velocity minimum was used for walk mean sd difference of 15 18 ms across horses and velocity zero crossing for trot mean sd difference from 4 14 to 12 7 ms depending on the condition the stride segmentation method also remained robust when applied to movement data of hind limb lame horses in future this method may find application in segmenting overground sensor data of various species

global smooth solution for the klein gordon zakharov equations in this paper the initial value problem to the klein gordon zakharov equations in two dimensions is discussed without assuming that the cauchy data are small we prove the existence and uniqueness of the global smooth solution for the problem via the so called continuous method and delicate a priori estimates also the asymptotic behaviour of the solution to the k g z equations with a small parameter approaching zero is studied

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered

on the existence and uniqueness of smooth solution for a generalized zakharov equation abstract the paper deals with the existence and uniqueness of smooth solution for a generalized zakharov equation we establish local in time existence and uniqueness in the case of dimension d 2 3 moreover by using the conservation laws and brezis gallouet inequality the solution can be extended globally in time in two dimensional case for small initial data besides we also prove global existence of smooth solution in one spatial dimension without any small assumption for initial data

numerical simulation for solitary wave of klein gordon zakharov equation based on the lattice boltzmann model abstract this work reports a study of klein gordon zakharov equation by using the lattice boltzmann method the klein gordon zakharov equation describes the interaction of the langmuir wave and the ion acoustic wave in plasma numerical simulations of the constructed lattice boltzmann model for the klein gordon zakharov equation show the propagation and the interaction of the 1 1 and 2 1 dimensional solitary waves these simulation results are examined and compared by using different parameters and different schemes this work indicates that the lattice boltzmann method can be a very effective tool for the simulation of klein gordon zakharov equation

a bilinear estimate with applications to the kdv equation u x 0 u0 x where u0 h r our principal aim here is to lower the best index s for which one has local well posedness in h r i e existence uniqueness persistence and continuous dependence on the data for a finite time interval whose size depends on u0 hs equation in 1 1 was derived by korteweg and de vries 21 as a model for long wave propagating in a channel a large amount of work has been devoted to the existence problem for the ivp 1 1 for instance see 9 10 the inverse scattering method applies to this problem and under appropriate decay assumptions on the data several existence results have been established see 5 6 14 28 33 another approach inherited from hyperbolic problems relies on the energy estimates and in particular shows that 1 1 is locally well posed in h r for s 3 2 see 2 3 12 29 30 31 using these results and conservation laws global in time well posedness in h r s 2 was established see 3 12 30 also global in time weak solutions in the energy space h r were constructed in 34 in 13 and 22 a local smoothing effect for solutions of 1 1 was discovered this combined with the conservation laws was used in 13 and 22 to construct global in time weak solutions with data in h r and even in l r in 16 we introduced oscillatory integral techniques to establish local well posedness of 1 1 in h r s 3 4 and hence global in time well posedness in h r s 1 in 16 we showed how to obtain the above mentioned result by picard iteration in an appropriate function space in 4 j bourgain introduced new function spaces adapted to the linear operator t 3 x for which there are good bilinear estimates for the nonlinear term x u 2 using these spaces bourgain was able to establish local well posedness of 1 1 in h r l r and hence by a conservation