Well posedness for the 1D Zakharov-Rubenchik system

zbMath1165.35448arXiv0809.1089MaRDI QIDQ1004329

Carlos Matheus, Felipe Linares

Publication date: 2 March 2009

Published in: Advances in Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.1089

zbMATH Keywords

global well posednesslocal well posednessZakharov-Rubenchik system

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (20)

Conservative compact difference scheme for the Zakharov–Rubenchik equations ⋮ Initial boundary value problem for generalized Zakharov equations with nonlinear function terms ⋮ Bifurcations and exact traveling wave solutions of the Zakharov-Rubenchik equation ⋮ Equations of Langmuir turbulence and Zakharov equations: smoothness and approximation ⋮ Initial Boundary Value Problem for a Generalized Zakharov Equations ⋮ On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system ⋮ A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov-Rubenchik equations ⋮ The time-periodic solutions to the modified Zakharov equations with a quantum correction ⋮ Lie symmetries and traveling wave solutions of the 3D Benney-Roskes/Zakharov-Rubenchik system ⋮ Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equations ⋮ Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov-Rubenchik equations ⋮ Initial boundary value problem for generalized Zakharov equations. ⋮ Uniform adiabatic limit of Benney type systems ⋮ Numerical methods and simulations for the dynamics of one-dimensional Zakharov-Rubenchik equations ⋮ Cauchy problem of the generalized Zakharov type system in \(\mathbf{R}^{2}\) ⋮ On long-time behavior of solutions of the Zakharov–Rubenchik/Benney–Roskes system ⋮ Two numerical methods for the Zakharov-Rubenchik equations ⋮ On global smooth solution for generalized Zakharov equations ⋮ On the Cauchy problem describing an electron-phonon interaction ⋮ Global existence for stochastic strongly dissipative Zakharov equations

This page was built for publication: Well posedness for the 1D Zakharov-Rubenchik system