Exact Traveling Wave Solutions to a Model for Solid-Solid Phase Transitions Driven by Configurational Forces

2011 ◽  
Vol 418-420 ◽  
pp. 1694-1697 ◽  
Author(s):  
Chang Hong Guo ◽  
Xiang Dong Liu ◽  
Shao Mei Fang
Keyword(s):  
Phase Transitions ◽  
Traveling Wave ◽  
Solid Phase ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Configurational Forces ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

This paper studies the exact traveling wave solutions to a model for solid-solid phase transitions driven by configurational forces. The model consists of the partial differential equations of linear elasticity coupled to a quasilinear nonuniformly parabolic equation of second order, which describes the diffusionless phase transitions of solid materials. By using the hyperbolic tangent function expansion method and homogeneous balance method, some exact traveling wave solutions, including solitary wave solutions are obtained for the phase transitions model in one space dimension.

scholarly journals New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhao Li ◽  
Tianyong Han
Keyword(s):  
Traveling Wave ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Ginzburg Landau ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended G ′ / G -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

scholarly journals Exact Traveling Wave Solutions to Benney- Luke Equation

2018 ◽  
Vol 37 ◽  
pp. 1-14
Author(s):  
Zahidul Islam ◽  
Mohammad Mobarak Hossain ◽  
Md Abu Naim Sheikh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

By using the improved (G¢/G) -expansion method, we obtained some travelling wave solutions of well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation. We show that the improved (G¢/G) -expansion method is a useful, reliable, and concise method to solve these types of equations.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 1-14

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