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New type of travelling wave solutions
Mathematical Methods in the Applied Sciences, 2003AbstractWe study the existence of combustion waves for an autocatalytic reaction in the non‐adiabatic case. Based on the fact that the reaction system has canard solutions separating the slow combustion regime from the explosive one, we prove by applying the geometric theory of singularly perturbed differential equations the existence of a new type of ...
Shchepakina, Elena A. +2 more
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Traveling Wave Solutions for a Combustion Problem
Studies in Applied Mathematics, 1989A simple model for combustion consisting of two parabolic equations is considered. It is shown that plane wave solutions exist. Certain invariant integrals are obtained, from which a nonexistence criterion is derived. The effect of the wave speed on the shape of the wave is deduced.
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Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions
Qualitative Theory of Dynamical Systems, 2017A traveling wave solution \(u= U(x-ct)\) of a partial differential equation \(u_{xx}= F(u,u_x,u_t)\) is called an algebraic traveling wave solution if there exists a polynomial \(p\) such that \(p(U,U')= 0\). The author completely characterizes the existence of algebraic traveling wave solutions of the partial differential equation \[ u_t= du_{xx}- a(u-
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A New Integrable Hierarchy, Parametric Solutions and Traveling Wave Solutions
Mathematical Physics, Analysis and Geometry, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiao, Zhijun, Li, Shengtai
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International Journal of Bifurcation and Chaos, 2019
For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of ...
Jibin Li, Guanrong Chen, Shengfu Deng
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For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of ...
Jibin Li, Guanrong Chen, Shengfu Deng
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TRAVELING WAVE SOLUTIONS OF THE GREEN–NAGHDI SYSTEM
International Journal of Bifurcation and Chaos, 2013We investigate the traveling wave solutions of the Green–Naghdi system. Using the qualitative analysis methods of planar autonomous systems, we show not only its phase portraits but also the exact expressions of some bounded wave solutions. These results are a complement of the work by Deng et al.
Deng, Shengfu +2 more
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Traveling-wave-type gravitational soliton solutions
International Journal of Theoretical Physics, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Exact Traveling‐Wave Solutions for Model Geophysical Systems
Studies in Applied Mathematics, 1990Exact traveling‐wave solutions of time‐dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems.
Sachdev, P. L., Gupta, Neelam
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Traveling Wave Solutions of Parabolic Systems
1994Part I. Stationary waves: Scalar equation Leray-Schauder degree Existence of waves Structure of the spectrum Stability and approach to a wave Part II. Bifurcation of waves: Bifurcation of nonstationary modes of wave propagation Mathematical proofs Part III.
Aizik Volpert +2 more
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Analytic approximations of travelling wave solutions
Applicable Analysis, 1994A method based on differential inequalities and the maximum principle is developed to construct analytic approdimations of travelling wave solutions of certain reaction–diffusion equations arising in biology. The approximations are asymptotic in the sense that they converge to the unique travelling wave on the real line as the wave speed goes to ...
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