A geometric approach for solving the density-dependent diffusion Nagumo equation

Abstract

In this paper, some solutions of the density-dependent diffusion Nagumo equation are obtained by using a new approach, the Lie symmetry group-preserving scheme (LSGPS). The effects of various model parameters on the solution are investigated graphically using LSGPS. Finally, a different reduction method of PDEs is applied to construct two new analytical solutions and a first integral of the Nagumo equation.

Chirped optical solitons and stability analysis of the nonlinear Schrödinger equation with nonlinear chromatic dispersion

“…In nonlinear sciences, the study of accurate solutions to nonlinear partial differential equations (NLPDEs) is important because physical processes in the real world may be efficiently described by applying the theory of mathematical tools [1,2]. NLPDEs have had a significant impact on applied science and engineering over the last two decades [3,4]. The study of the soliton solutions explores a theoretical reference for the research of nonlinear physical models, soliton control, optical switching equipment and so on.…”

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].…”

New Results on the Equivalence of K -Functionals and Modulus of Continuity of Functions Defined on the Sobolev Space Constructed by the Generalized Jacobi-Dunkl Operator

“…The translation operator f ðxÞ ↦ f ðx + yÞ is used for the construction of modulus of continuity and smoothness which are the fundamental elements in the classical theory of the approximation of functions on ℝ (see [3][4][5]).…”