We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive Sq entropies. Our present contribution is in line with recent developments, where nonlinear extensions inspired on the q-thermostatistical formalism have been proposed for the Schroedinger, Klein–Gordon, and Dirac wave equations. These previously introduced equati...

Motivated by Benney’s general theory, we propose new models for short wave long wave interactions when the long waves are described by nonlinear systems of conservation laws. We prove the strong convergence of the solutions of the vanishing viscosity and short wave long wave interactions systems by using compactness results from the compensated compactness theory and new energy estimates obtain...

The superharmonic instability is pervasive in large-amplitude water-wave problems and numerical simulations have predicted a close connection between it and crest instabilities and wave breaking. In this paper we present a nonlinear theory, which is a generic nonlinear consequence of superharmonic instability. The theory predicts the nonlinear behaviour witnessed in numerics, and gives new info...

In this paper, guided wave health monitoring in plate structure for detection of nonlinear contact scatter is conduct using vibration modulation technique. By time-frequency analysis of modulated guided wave series, the nonlinear responses at frequency of vibration are extracted out and used for defect imaging. It is shown that the nonlinear guided wave imaging method based on vibration modulat...

The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary d...

Nonlinear transfer from wave-wave i n teractions is an important term in the action-balance equation governing t h e e v olution of the surface-gravity-wave eld. Computation of this term, however, has hitherto been so consuming of computer resources that its full representation has not been feasible in nonparametric two-dimensional computer models of this e q u ation. This paper describes the i...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

ABSTRACT Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modif...