Spacial inhomogeneity and nonlinear tunneling for the forced KdV equation

KAM for quasi-linear and fully nonlinear forced KdV

We prove the existence of quasi-periodic, small amplitude, solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities we also obtain the linear stability of the solutions. The proofs are based on a combination of different ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization proce...

Nonlinear superposition Formulae for supersymmetric KdV Equation

In this paper, we derive a Bäcklund transformation for the supersymmetric Kortwegde Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Kortweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 1984....

Unconditionally Stable Difference Scheme for the Numerical Solution of Nonlinear Rosenau-KdV Equation

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

Forced Vibrations for a Nonlinear Wave Equation

Application of the Kudryashov method and the functional variable method for the complex KdV equation

In this present work, the Kudryashov method and the functional variable method are used to construct exact solutions of the complex KdV equation. The Kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.