Using a Miura-Gardner-Kruskal type construction, we show that the Camassa-Holm equation has an infinite number of local conserved quantities. We explore the implications of these conserved quantities for global well-posedness.

Abstract: The Restrictive Taylor Approximation is implemented to find numerical solution of linear and nonlinear partial differential equation. In this paper we introduce the numerical solution of Gardner equation and General KdV equation, also we study the stability of both equations. The scheme is based on evaluation the restrictive term at the first solution level and then applies the formul...

Using the relation established by Johnson–Zumbrun between Hill’s method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic Evans function given by the 2-modified characteristic Fredholm determinant of an associated Birman–Schwinger system, together with a Volterra integral computation introduced by Gesztesy–Makarov, we give an explicit con...

The adiabatic decay of different types of internal wave solitons caused by the Earth’ rotation is considered within the framework of the Gardner–Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions. It is shown that at the early stage of evolution solitons gradually decay under the i...

In this study, the meshless collocation approach is used to determine numerical solution generalized time-fractional Gardner equation. The Crank-Nicolson technique approximate space derivatives, whereas Caputo derivative of fractional order first time derivative. solutions, which show method?s efficacy and accuracy, are pro?vided discussed. shows that our method effective in producing extremely...

This study investigates exact analytical solutions of some nonlinear partial differential equations arising in mathematical physics. To this reason, the Kudryashov-Sinelshchikov equation, ZK-BBM equation and Gardner have been considered. With implementation trial solution algorithm, solitary wave, bright, dark periodic traveling wave considered attained. The checked graphs given via package pro...