Long-time behavior of solutions to the general class of coupled nonlocal nonlinear wave equations

Asymptotic behavior of solutions to PDEs (35B40) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Soliton solutions (35C08) Integro-partial differential equations (35R09)

Cites Work

Petviashvilli's method for the Dirichlet problem
Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations
Existence and uniqueness of solutions to initial boundary value problem for the higher order Boussinesq equation
Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations
On the convergence of the nonlocal nonlinear model to the classical elasticity equation
Higher order dispersive effects in regularized Boussinesq equation
Numerical approximation to Benjamin type equations. Generation and stability of solitary waves
Petviashvili type methods for traveling wave computations. II: Acceleration with vector extrapolation methods
Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I: Approximations
A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
On a theory of nonlocal elasticity of bi-Helmholtz type and some applications
Petviashvili type methods for traveling wave computations. I: Analysis of convergence
On a Toda lattice model with a transversal degree of freedom
A <scp>F</scp>ourier pseudospectral method for a generalized improved <scp>B</scp>oussinesq equation
The Cauchy problem for coupled IMBq equations
A higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity
Blow up of solutions of a generalized Boussinesq equation
Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations
An efficient method to compute solitary wave solutions of fractional Korteweg–de Vries equations
Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
Solitary waves in a diatomic lattice: Analytic approximations for a wide range of speeds by quasi-continuum methods
Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity
Error analysis of the exponential wave integrator sine pseudo-spectral method for the higher-order Boussinesq equation

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