Boussinesq equations: M-fractional solitary wave solutions and convergence analysis

The studies of the dynamics behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. This study investigates the nonlinear fractional modified Boussinesq equation and the fractional bad Boussinesq equation using the extended sinh-Gordon equation expansion method. Several travelling wave solutions are successfully constructed. By choosing suitable values of parameters, the 2D and 3D graphs of the reported solutions are successfully plotted. The convergence analysis of the applied method is also discussed. Keywords: The Sinh-Gordon equation, Boussinesq equations, Solitons, M-fractional derivative, Convergence analysi

The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given

On the wave solutions to the TRLW equation

In this study, a nonlinear model is investigated, namely; the time regularized long wave equation. Various solitary wave solutions are constructed such as the non-topological, compound topological-non-topological bell-type, singular and compound singular soliton solutions. Under the choice of suitable parameters values, the 2D and 3D graphs to all the obtained solutions are plotted. The reported results in this study may be helpful in explaining the physical meanings of some important nonlinear models arising in the field of nonlinear science

On the wave solutions to the TRLW equation

In this study, a nonlinear model is investigated, namely; the time regularized long wave equation. Various solitary wave solutions are constructed such as the non-topological, compound topological-non-topological bell-type, singular and compound singular soliton solutions. Under the choice of suitable parameters values, the 2D and 3D graphs to all the obtained solutions are plotted. The reported results in this study may be helpful in explaining the physical meanings of some important nonlinear models arising in the field of nonlinear science

On the exact solitary wave solutions to the long-short wave interaction system

In this paper, the application of the simplified the extended sinh-Gordon equation expansion method to the long-short-wave interaction system. We successfully construct various solitary wave solutions to this nonlinear complex model. The long-short-wave interaction system describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The 2D and 3D surfaces to some of the obtained solutions are plotted

Construction of various soliton solutions via the simplified extended sinh-Gordon equation expansion method

In this paper, we present the simplified version of the extended sinh-Gordon equation expansion method. The newly proposed approach is based on the well-known sinh-Gordon equation and a travelling wave transformation. We successfully employed this approach to the (2+1)-dimensional nonlinear Chiral Schrodinger's and various solitary wave solutions to the studied nonlinear model are successfully constructed. The (2+1)-dimensional nonlinear Chiral Schrodinger's equation describes the edge states of the fractional quantum hall effect. The 2D and 3D surfaces of some of the obtained solutions are plotted

Optical solitons to the fractional Schrödinger-Hirota equation

This study reaches the dark, bright, mixed dark-bright, and singular optical solitons to the fractional Schrödinger-Hirota equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. Dark soliton describes the solitary waves with lower intensity than the background, bright soliton describes the solitary waves whose peak intensity is larger than the background, and the singular soliton solutions is a solitary wave with discontinuous derivatives; examples of such solitary waves include compactions, which have finite (compact) support, and peakons, whose peaks have a discontinuous first derivative. The constraint conditions for the existence of valid solutions are given. We use some suitable values of the parameters in plotting 3-dimensional surfaces to some of the reported solutions

On Some Complex Aspects of the (2+1)-dimensional Broer-Kaup-Kupershmidt System

The improved Bernoulli sub-equation function method is used in extracting some new exponential function solutions to the (2+1)-dimensional Broer-Kaup-Kupershmidt system. It is of vital effort to look for more solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt system, which are very helpful for coastal and civil engineers to apply the nonlinear water models in a harbor and coastal design. All the obtained solutions satisfied the (2+1)-dimensional Broer-Kaup-Kupershmidt system. The two- and three-dimensional shapes of all the obtained solutions in this paper are also presented. All the computations and the graphics plots in this study are carried out with the aid of the Wolfram Mathematica 9

Optical Solitons and Other Solutions to the (2+1)-Dimensional Cubic Nonlinear Schrödinger Equation with Fractional Temporal Evolution

In this study, the (2+1)-dimensional cubic nonlinear Schrödinger equation with fractional temporal evolution is investigated by using the extended sinh-Gordon equation expansion method. The idea of conformable fractional derivative is used in transforming the complex nonlinear partial differential equation to nonlinear ordinary differential equation. Dark, bright, mixed dark-bright, singular, mixed singular solitons and singular periodic wave solutions are successfully reached. The parametric conditions for the existence of valid solitons are given. The 2D and 3D graphics to some of the reported solutions are plotted

Regarding the numerical solutions of the Sharma-Tasso-Olver equation

With aid of the Wolfram Mathematica package, this study investigates the solutions of a nonlinear model with strong nonlinear- ity, namely; the Sharma-Tasso-Olver equation. We use the improved Bernoulli sub-equation function method in acquiring the analytical so- lution to this equation, we successfully obtain one-singular soliton so- lution with exponential function structure. Through the obtained ana- lytical solution, the finite forward difference method is used in approx- imating the exact and numerical solutions to this equation. We check the stability of the finite forward difference method with this equation using the Fourier-Von Neumann stability analysis. We find the L2 and L∞ norm error to the numerical approximation. We present the in- teresting 3D and 2D figures of the obtained singular soliton solution. We also plot the graphics of the numerical error, exact and numeri- cal approximations data obtained in this study by using the MATLAB package