New groups of solutions to the Whitham-Broer-Kaup equation

The Whitham-Broer-Kaup model is widely used to study the tsunami waves. The classical Whitham-Broer-Kaup equations are re-investigated in detail by the generalized projective Riccati-equation method. 20 sets of solutions are obtained of which, to the best of the authors’ knowledge, some have not been reported in literature. Bifurcation analysis of the planar dynamical systems is then used to show different phase portraits of the traveling wave solutions under various parametric conditions.

Optical solitons of space-time fractional Fokas–Lenells equation with two versatile integration architectures

Nonlinear Schrödinger’s equation and its variation structures assume a significant job in soliton dynamics. The soliton solutions of space-time fractional Fokas–Lenells equation with a relatively new definition of local M-derivative have been recovered by utilizing improved $\tan (\frac{\phi (\eta )}{2})$ tan ( ϕ ( η ) 2 ) -expansion method and generalized projective Riccati equation method. The obtained solutions are periodic, dark, bright, singular, rational, along with few forms of combo-soliton solutions. These solutions are given under constraints conditions which ensure their existence. The impact of local fractional parameter is featured by its graphical portrayal. 2D and 3D diagrams are drawn to illustrate the efficacy of the conformable fractional order on the behavior of some of those solutions. The secured solutions of this model have dynamic and significant justifications for some real-world physical occurrences. Our study shows that the suggested schemes are effective, reliable, and simple for solving different types of nonlinear differential equations.

Explicit solutions of the (2 + 1)-dimensional Hirota–Maccari system arising in nonlinear optics

In this paper, new exact traveling wave solutions of the [Formula: see text]-dimensional Hirota–Maccari system arising in nonlinear optics are successfully obtained by using two methods, namely, Improved [Formula: see text]-expansion method and general projective Riccati equation method. The considered methods have been successfully implemented to find exact traveling wave solutions for nonlinear evaluation equations (NLEE) coming for describing nonlinear optics. The results obtained by these methods are straightforward and concise mathematical tool to set up the exact solutions of NLEE.

Solitary wave solutions of two KdV-type equations

The present paper investigates the solitary wave solutions of the nonlinear evolution equations with power nonlinearties. The study has been carried out for two examples of KdV-type equations, namely, the nonlinear dispersive equation and the generalised KdV equation. To achieve our goal, we have applied the projective Riccati equation method. As a result, many exact solutions in the form of solitary wave solutions and combined formal solitary wave solutions are obtained

KAJIAN TENTANG METODE PERSAMAAN RICCATI PROYEKTIF

In this paper, we discuss the derivation and application of a projective Riccatiequation method in solving nonlinear partial dierential equations. We also study themathematical aspects of the method and its limitations in some particular cases.Kata Kunci: Nonlinear partial dierential equations, projective Riccati equation method,dominant balance principle

A modified generalized projective Riccati equation method

A modification of the generalized projective Riccati equation method is proposed to treat some nonlinear evolution equations and obtain their exact solutions. Some known methods are obtained as special cases of the proposed method. In addition, the method is implemented to find new exact solutions for the well-known Dreinfelds-Sokolov-Wilson system of nonlinear partial differential equations.

Exact Solutions to KdV6 Equation by Using a New Approach of the Projective Riccati Equation Method

We study a new integrable KdV6 equation from the point of view of its exact solutions by using an improved computational method. A new approach to the projective Riccati equations method is implemented and used to construct traveling wave solutions for a new integrable system, which is equivalent to KdV6 equation. Periodic and soliton solutions are formally derived. Finally, some conclusions are given.