Exact solutions of variable coefficient nonlinear diffusion–reaction equations with a nonlinear convective term

Mishra, Ajay; Kumar, Rajesh

doi:10.1016/j.physleta.2010.03.039

Cited by 20 publications

(19 citation statements)

References 12 publications

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“…The dispersion term stretches the solitary wave, gradually elongating it until the solitary wave vanishes. On the contrary, the solitary wave is compressed into be a steeper and steeper one by the nonlinear convection term [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Orbital stability and dynamical behaviors of solitary waves for the Camassa–Holm equation with quartic nonlinearity

Yin

Xing

2015

Chaos, Solitons & Fractals

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Section: Introductionmentioning

confidence: 99%

Orbital stability and dynamical behaviors of solitary waves for the Camassa–Holm equation with quartic nonlinearity

Yin

Xing

2015

Chaos, Solitons & Fractals

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“…The wave front head is at z = 0. It is readily verified that (5) solves (4) with the dispersion relation…”

Section: Setting the Stage: An Example From Population Dynamicsmentioning

confidence: 95%

“…The first-order term represents a constant convective velocity, which only shifts the propagation velocity. We therefore retain the quadratic term and write h(u) = ku 2 /2 [4][5][6], where k is a positive dimensionless constant.…”

Section: Setting the Stage: An Example From Population Dynamicsmentioning

confidence: 99%

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BLUES function method in computational physics

Indekeu¹,

Müller-Nedebock²

2018

J. Phys. A: Math. Theor.

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We introduce a computational method in physics that goes "beyond linear use of equation superposition" (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green's function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

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“…Mishra and Kumar [11] introduced the exact solutions for a variable coefficient nonlinear diffusion-reaction equation with a nonlinear convective term. In this model, the authors found the solitary wave equation and this type of equation is arisen in a variety of contexts in physical and biological problems.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study of the Nonlinear Reaction-Diffusion Equation with Different Type of Absorbent Term by Homotopy Analysis Method

Gupta

Verma

2012

Zeitschrift Für Naturforschung A

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In this paper, based on the homotopy analysis method (HAM), a new powerful algorithm is used for the solution of the nonlinear reaction-diffusion equation. The algorithm presents the procedure of constructing a set of base functions and gives the high-order deformation equation in a simple form. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of the solution series by introducing an auxiliary parameter h. The solutions of the problem of presence and absence of absorbent term and external force for different particular cases are presented graphically.

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Exact solutions of variable coefficient nonlinear diffusion–reaction equations with a nonlinear convective term

Cited by 20 publications

References 12 publications

Orbital stability and dynamical behaviors of solitary waves for the Camassa–Holm equation with quartic nonlinearity

Orbital stability and dynamical behaviors of solitary waves for the Camassa–Holm equation with quartic nonlinearity

BLUES function method in computational physics

A Numerical Study of the Nonlinear Reaction-Diffusion Equation with Different Type of Absorbent Term by Homotopy Analysis Method

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