On some new travelling wave structures to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model

In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model representing the wave propagation through incompressible fluids.The linearization of the wave structure in shallow water necessitates more critical wave capacity conditions than it does in deep water,and the strong nonlinear properties are perceptible.Some novel travelling wave solutions have been observed including solitons,kink,periodic and rational solutions with the aid of the latest computing tools such as Mathematica or Maple.The physical and analytical properties of several families of closed-form solutions or exact solutions and rational form function solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model problem are examined using Mathematica.

Lump and travelling wave solutions of a(3+1)-dimensional nonlinear evolution equation

In this paper,the(3+1)-dimensional nonlinear evolution equation is studied analytically.The bilinear form of given model is achieved by using the Hirota bilinear method.As a result,the lump waves and col-lisions between lumps and periodic waves,the collision among lump wave and single,double-kink soliton solutions as well as the collision between lump,periodic,and single,double-kink soliton solutions for the given model are constructed.Furthermore,some new traveling wave solutions are developed by applying the exp(−φ(ξ))expansion method.The 3D,2D and contours plots are drawn to demonstrate the nature of the nonlinear model for setting appropriate set of parameters.As a result,a collection of bright,dark,periodic,rational function and elliptic function solutions are established.The applied strategies appear to be more powerful and efficient approaches to construct some new traveling wave structures for various contemporary models of recent era.

New soliton wave solutions of a(2+1)-dimensional Sawada-Kotera equation

In this work,we studied a(2+1)-dimensional Sawada-Kotera equation(SKE).This model depicts non-linear wave processes in shallow water,fluid dynamics,ion-acoustic waves in plasmas and other phe-nomena.A couple of well-established techniques,the Bäcklund transformation based on the modified Kudryashov method,and the Sardar-sub equation method are applied to obtain the soliton wave solution to the(2+1)-dimensional structure.To illustrate the behavior of the nonlinear model in an appealing fashion,a variety of travelling wave solutions are formed,such as contour,2D,and 3D plots.The pro-posed approaches are proved more convenient and dominant for getting analytical solutions and can also be implemented to a variety of physical models representing nonlinear wave phenomena.

On global behavior for complex soliton solutions of the perturbed nonlinear Schrödinger equation in nonlinear optical fibers

In this research article,the perturbed nonlinear Schrödinger equation(P-NLSE)is examined by utilizing two analytical methods,namely the extended modified auxiliary equation mapping and the generalized Riccati equation mapping methods.Consequently,we establish several sorts of new families of complex soliton wave solutions such as hyperbolic functions,trigonometric functions,dark and bright solitons,periodic solitons,singular solitons,and kink-type solitons wave solutions of the P-NLSE.Using the mentioned methods,the results are displayed in 3D and 2D contours for specific values of the open parameters.The obtained findings demonstrate that the implemented techniques are capable of identifying the exact solutions of the other complex nonlinear evolution equations(C-NLEEs)that arise in a range of applied disciplines.