On the Integrability of a Class of Nonlinear Dispersive Wave Equations
نویسنده
چکیده
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.
منابع مشابه
Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.
متن کاملLinear Superposition in Nonlinear Wave Dynamics
We study nonlinear dispersive wave systems described by hyperbolic PDE’s in Rd and difference equations on the lattice Zd. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi–Pas...
متن کاملNumerical Solution of Some Nonlocal, Nonlinear Dispersive Wave Equations
We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usuall...
متن کاملThe Attractor on a Class of Viscous Nonlinear Dispersive Wave Equations
Abstract: This paper aims at presenting a proof of the attractor for a class of viscous nonlinear dispersive wave equations. In this paper, the global existence of solution to this equation in L2 under the periodical condition is studied. By using the time estimate of this equation, we get the compact and bounded absorbing set and the existence of the global attractor for the viscous nonlinear ...
متن کاملAnalyticity of the Scattering Operator for Semilinear Dispersive Equations
We present a general algorithm to show that a scattering operator associated to a semilinear dispersive equation is real analytic, and to compute the coefficients of its Taylor series at any point. We illustrate this method in the case of the Schrödinger equation with powerlike nonlinearity or with Hartree type nonlinearity, and in the case of the wave and Klein–Gordon equations with power nonl...
متن کامل