The Exact Solutions of the Conformable Time-Fractional Modified Nonlinear Schrödinger Equation by the Trial Equation Method and Modified Trial Equation Method [PDF]
Advances in Mathematical Physics, 2022 Using the trial equation method (TEM) and modified trial equation method (MTEM), firstly, we find the analytical solutions of the conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE), and finally, we present numerical results in
Safoura Rezaei Aderyani +3 more
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Extended trial equation method to generalized nonlinear partial differential equations
Applied Mathematics and Computation, 2013 In this article, we give the extended trial equation method for solving nonlinear partial differential equations with higher order nonlinearity. By use of this method, the exact traveling wave solutions including soliton solution, singular soliton solutions, rational function solution and elliptic integral function solution to one-dimensional general ...
Mehmet Ekici +2 more
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Traveling wave solutions of a coupled Schrödinger-Korteweg-de Vries equation by the generalized coupled trial equation method [PDF]
Heliyon, 2023 The coupled Schrödinger-Korteweg-de Vries equation is a critical system of in nonlinear evolution equations. It describes various processes in dusty plasma, such as Langmuir waves, dust-acoustic waves, and electromagnetic waves.
Jiaxin Shang, Wenhe Li, Da Li
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The Extended Trial Equation Method for Some Time Fractional Differential Equations [PDF]
Discrete Dynamics in Nature and Society, 2013 Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the ...
Yusuf Pandir +2 more
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The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation [PDF]
Abstract and Applied Analysis, 2013 The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give
Hasan Bulut +2 more
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Nonlinear Engineering, 2021 This article obtains optical solitons to the Biswas-Arshed equation for birefringent fibers with higher order dispersions and in the absence of four-wave mixing terms, in a media with Kerr type nonlinearity.
Tahir Muhammad +2 more
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Dispersive optical solitons with Schrödinger–Hirota equation by extended trial equation method [PDF]
Optik, 2017 Abstract This paper obtains bright, dark and singular soliton solutions from perturbed Schrodinger–Hirota equation that governs the propagation of dispersive pulses through optical fibers. The trial equation method is adopted to achieve this goal. Both Kerr and power laws of nonlinearity are covered.
Qin Zhou +2 more
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Trial Equation Method for Solving the Improved Boussinesq Equation
Advances in Pure Mathematics, 2014 Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact
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Application of Trial Equation Method for Solving the Benjamin Ono Equation
Journal of Applied Mathematics and Physics, 2014 In the article, the nonlinear equation is reduced to an ordinary differential equation under the travelling wave transformation. Using trial equation method, the ODE is reduced to the elementary integral form. In the end, complete discrimination system for polynomial is used to solve the corresponding integrals and obtain the classification of all ...
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Analytical evaluations using neural network-based method for wave solutions of combined Kairat-II-X differential equation in fluid mechanics [PDF]
Scientific ReportsIn this paper, a symbolic computation method based on a neural network architecture, the improved neural network-based method, for obtaining novel exact solutions to combined Kairat-II-X differential equation is proposed.
Ping Zhou +8 more
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