Abstract In the present study, ion-acoustic solitary wave solutions for Kadomtsev–Petviashvili (KP) equation, potential KP and Gardner equation are constructed. The nonlinear equations studying process of waves without collisions plasma having non-isothermal electrons cold ions. Two-dimensional (IASWs) in magnetized consisting We obtained same as dark bright, kink anti-kink solitons. physical p...

Abstract In this paper, we investigate the modified Kadomtsev–Petviashvili-II (mKP-II) equation, which has important applications in fluid dynamics, plasma physics and electrodynamics. By utilizing Hirota bilinear method, N-soliton solutions of mKP-II equation are obtained. The resonance Y-type soliton, interaction between M-resonance solitons P-resonance constructed by imposing some constraint...

Extended shallow water wave equations are derived, using the method of asymptotic expansions, from Euler (or wave) equations. These extended models valid one order beyond usual weakly nonlinear, long approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive Korteweg–de Vries (KdV) equation, then proceed with Benjamin–Bona–Mahony Camassa–Holm in (...

We introduce and solve the non-commutative version of Hermite-Pad\'{e} type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to subclass solutions Hirota (discrete Kadomtsev--Petviashvili) system its linear also prove integrability constrained system, which simplest case is discrete-time Toda lattice equation known from theory Pad\'{e} approximants m...