Our aim in this article to constructed the new solitary wave solutions of (2+1)-dim nonlinear Nizhnik-Novikov-Vesselov equation by novel approach which is extended modified rational expansion method. The new solitary wave solutions are rational, trigonometric, hyperbolic, elliptic functions including dark, bright, singular, combined, optical solitons, kink wave, anti-kink wave, periodic wave, travelling wave and we also represent the physical interpretation of new solutions by 2D and 3D graphical by using the Mathematica. These constructed solutions may play vital role in the areas of Mathematical physics, plasma physics, nonlinear optics, quantum mechanics, fluid dynamics and many different fields of applied sciences. The complete calculations show that this new technique is more powerful, effective, straightforward and we can also apply on other nonlinear PDEs involves in Mathematical physics and many other physical sciences.

Propagation of long internal waves in density stratified ocean for the (2+1)-dimensional nonlinear Nizhnik-Novikov-Vesselov dynamical equation

Biswas–Arshed equation with the beta time derivative: Optical solitons and other solutions

Optical wave structures to the Fokas–Lenells equation

Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid solutions to a (3+1)-dimensional shallow water wave equation with time-dependent coefficients

The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2 + 1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.

The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions

Chirp-free optical solitons in fiber Bragg gratings with dispersive reflectivity having polynomial law of nonlinearity

In this paper, we studied Kaup–Newell (KN) equation in coupled vector form without four-wave mixing terms in birefringent fibers. We employed Jacobi elliptic function expansion method in order to demonstrate sub-pico-second optical soliton solutions. Beside bright and dark solitons, Jacobi elliptic function solutions and hyperbolic solutions are obtained. Moreover, the graphs for some solution are presented.

Optical solitons and other solutions to Kaup–Newell equation with Jacobi elliptic function expansion method

The propagation of small amplitude long capillary–gravity waves on the surface of shallow water described by the higher order nonlinear Boussinesq type wave equation. This model is arising in mathematical physics, shallow water waves, fluid dynamics and fluid flow. We applied the modified Jacobi elliptic function expansion method to obtained exact solutions in the type of solitary wave and elliptic functions solutions. These solutions helps the mathematicians and physicians to understand the physical phenomena of this model. This technique can be utilized on other models to launch further exclusively novel solutions for other categories of nonlinear PDEs occurring in mathematical Physics.

Wafaa B. Rabie

Papers

Chirp-free optical solitons in fiber Bragg gratings with dispersive reflectivity having polynomial law of nonlinearity

Optical solitons and other solutions to Kaup–Newell equation with Jacobi elliptic function expansion method

Dispersive and propagation of shallow water waves as a higher order nonlinear Boussinesq-like dynamical wave equations

Optical solitons and other solutions in birefringent fibers with Biswas-Arshed equation by Jacobi's elliptic function approach

Optical solitons with differential group delay for coupled Kundu–Eckhaus equation using extended simplest equation approach