in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

We study the inverse scattering problem for the three dimensional nonlinear Schrödinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.

this paper studies the biswas-milovic equation with log law nonlinearity. thegausson solution is obtained by the ansatz method. subsequently, theconservation laws are derived and the conserved quantities are computed usingthe gausson solution.

in this paper, the homotopy analysis method (ham) is considered to obtain the solution of the schrodinger equation with a power law nonlinearity. for this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region...

Consider the ordinary diierential equation _ xt = F , x t ; x 0 = x 0 : 1 A solution 1 on 0; T , T T 0, to 1 is a continuously diierentiable function x : : 0 ; T !R n satisfying xt = x 0 + Z t 0 F , x s ds: We m a y ask for which functions F there exist a solution to 1 and, if so, if the solution is unique. Is it, for instance, suucient that F is a continuous function? The answer is no concerni...

This paper studies the Biswas-Milovic equation with log law nonlinearity. TheGausson solution is obtained by the ansatz method. Subsequently, theconservation laws are derived and the conserved quantities are computed usingthe Gausson solution.

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...

We consider the nonlinear Schrodinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons.