Traveling, periodic and localized solitary waves solutions of the (4+1)-dimensional nonlinear Fokas equation

Abstract

By utilizing the three distinctive approaches specifically, the extended Fan sub-equation method, the exp[−G()]-function expansion method, and the fractional transformation method, the traveling waves and soliton solutions of the (4+1)-dimensional nonlinear Fokas equation are extracted. Meanwhile, some parametric constraint conditions are described. The acquired solutions are singular and nonsingular soliton solutions, periodic solutions, breather solution, rational solutions, trigonometric periodic wave solutions, hyperbolic solutions, Weierstrass, and Jacobi elliptic doubly periodic wave solutions. The dynamics of some of the obtained solutions are investigated and described in 2-dimensional figures by choosing appropriate parameter values. The comparison of our obtained results with the other solutions in literature shows that the obtained solutions of this paper are new and have not been formulated before by other techniques. We believe that all these results are useful to enrich the knowledge of the important physical phenomenon characterized by the Fokas equation. The reported solutions illustrate the straightforwardness, reliability, and effectiveness of the used techniques that can be further employed to higher-dimensional nonlinear evolution equations.

Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

“…The results are exhibited after a comprehensive analysis of the mathematical procedures that are detailed in the rest of the paper. Finally, there are many methods to discuss solutions to partial differential equations (PDEs), which have many applications in physics [27][28][29][30][31][32][33][34][35][36].…”

“…These soliton molecules form the information transporter across intercontinental distances around the world. Lastly, the nonlinear Schrödinger's equation (NLSE) has been discussed with help of many models [1–32, 33–36]. The aspect of stochastically is one of the features that is less touched, and there are a few papers that have discussed this aspect [3–9].…”

Research on sensitivity analysis and traveling wave solutions of the (4 + 1)-dimensional nonlinear Fokas equation via three different techniques

“…Zang and Xia discovered the soliton solutions of the equation [25]. Khatri et al have utilized three distinctive approaches to find traveling wave solutions of given equation [26]. Khatri et al investigated a family of localized soliton and exact traveling solutions of this equation via distinct different methods, such as the Padés type transformation, the Jacobian-function method, triangle function approach or sine-cosine as well as the semi-inverse variational approach.…”