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Travelling Wave Solutions of the General Regularized Long Wave Equation
Qualitative Theory of Dynamical Systems, 2021This paper studies the model of the general regularized long wave (GRLW) equation. The main contribution of this paper is to find that GRLW equation has extra kink and anti-kink wave solutions when $p = 2n + 1$, while it's not for $p = 2n$. The authors give the phase diagram and obtained possible exact explicit parametric representation of the ...
Hang Zheng +3 more
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Traveling wave solutions for reaction–diffusion systems
Nonlinear Analysis: Theory, Methods & Applications, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Zhigui +2 more
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Physica Scripta
This paper presents a new study that incorporates the Stratonovich integral and conformal fractional derivative into the fractional stochastic Bogoyavlenskii equation with multiplicative noise.
T. Han, Yueyong Jiang
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This paper presents a new study that incorporates the Stratonovich integral and conformal fractional derivative into the fractional stochastic Bogoyavlenskii equation with multiplicative noise.
T. Han, Yueyong Jiang
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Mathematical methods in the applied sciences, 2020
In this work, the generalized Kudryashov method is used to obtain the exact traveling wave solutions for two important nonlinear evolution equations, the Chaffee–Infante equation in (2 + 1)‐dimensions and the dimensionless Zakharov equation.
Muhammad Tahir +5 more
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In this work, the generalized Kudryashov method is used to obtain the exact traveling wave solutions for two important nonlinear evolution equations, the Chaffee–Infante equation in (2 + 1)‐dimensions and the dimensionless Zakharov equation.
Muhammad Tahir +5 more
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Traveling-wave solutions to thin-film equations
Physical Review E, 1993Thin films can be effectively described by the lubrication approximation, in which the equation of motion is ${\mathit{h}}_{\mathit{t}}$+(${\mathit{h}}^{\mathit{n}}$${\mathit{h}}_{\mathit{x}\mathit{x}\mathit{x}}$${)}_{\mathit{x}}$=0. Here h is a necessarily positive quantity which represents the height or thickness of the film.
, Boatto, , Kadanoff, , Olla
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Modern physics letters B, 2019
In this paper, the extended rational sinh-cosh method (ERSCM) and modified Khater method are applied to the biological population model to derive new exact solutions.
H. Rezazadeh +5 more
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In this paper, the extended rational sinh-cosh method (ERSCM) and modified Khater method are applied to the biological population model to derive new exact solutions.
H. Rezazadeh +5 more
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Traveling Wave and Multiple Traveling Wave Solutions of Parabolic Equations
SIAM Journal on Mathematical Analysis, 1982We consider scalar equations $u_t = f(u_{xx} ,u_x ,u)$ with $\frac{\partial }{{\partial \alpha }}f(\alpha ,\beta ,\gamma ) \geq 1$. We first determine the stability of the monotonic traveling wave solutions $u(t,x) = \phi (x - ct,c)$. We then study the continued existence and bifurcations of these solutions as the wavespeed c varies.
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Travelling Wave Solutions for sine-Gordon Prototypes
International Journal of Nonlinear Sciences and Numerical Simulation, 2001Summary: By using finite difference discretization for the sine-Gordon equation, we obtain the sine-Gordon prototypes. For these prototypes, the existence of discrete periodic travelling wave solutions and discrete solitons are proved by the anti-integrable limit method.
Zheng, Yongai +2 more
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Explicit travelling-wave solutions
2004A number of explicit nontrivial monotonic travelling-wave solutions of the nonlinear reaction-convection-diffusion equation (1.1) have been discovered by various authors. It is not the intention here to provide a survey of all these. However, a few remarks on the possibilities offered by the now apparent correspondence between travelling-wave solutions
Brian H. Gilding, Robert Kersner
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Periodic travelling-wave solution of brusselator
Acta Mathematicae Applicatae Sinica, 1988The author firstly gives the conditions such that a quartic algebraic equation has a pair of complex conjugate roots and a pair real roots, and all of the roots have strictly negative real part (Lemma 1-3). With that, he gives the conditions of coefficients of the characteristic equation which enables us to know the existence of the Hopf bifurcation ...
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