Abstract. We analyze a heuristic numerical method suggested by V.I. Petviashvili in 1976 for approximation of stationary solutions of nonlinear wave equations. The method is used to construct numerically the solitary wave solutions, such as solitons, lumps, and vortices, in a space of one and higher dimensions. Assuming that the stationary solution exists, we find conditions when the iteration ...

In the present study, natural transform iterative method (NTIM) has been implemented for solution of a fractional Zakharavo–Kuznetsov (FZK) equation. NTIM is relatively new technique handling non-linear differential equations. The tested upon two FZK equalities. proposed compared with existing perturbation–iteration algorithm (PIA) and residual power series (RPSM). From numerical results, it cl...

Deterministic and stochastic nonlinear partial differential equations with mixed features (e.g. partial hyperbolicity and anisotropicity) have played an important role in describing the models in physics, chemistry, finance and other real-world phenomena. Moreover, sitting at the interface between probability theory, mathematical analysis and theory of parabolic and hyperbolic partial different...

In this paper, a singularity structure analysis of the (2+1)-dimensional Zakharov equation is carried out and it is shown that it admits the Painleve property. The bilinear form of this equation is derived from the Painleve analysis in a straightforward manner. Using this bilinear form, we have constructed the simply one soliton solution by the Hirota method. We have then presented the localize...

Nonlinear ion-acoustic waves are analyzed in a nonrelativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary temperature. Quantum diffraction is described by a modified Bohm potential consistent with finite-temperature quantum kinetic theory in the long-wavelength limit...