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Unveiling chaos and stability in advection diffusion reaction systems via advanced dynamical and sensitivity analysis. [PDF]
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KdV Equations and Integrability Detectors
Acta Applicandae Mathematicae, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grammaticos, B. +2 more
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Reduction of KdV and Cylindrical KdV Equations to Painlevé Equation
Journal of the Physical Society of Japan, 1982Similarity solutions of the KdV and cylindrical KdV equations are studied by means of Lie's method of infinitesimal transformation groups. It is shown that the KdV equation is reduced to the Painleve transcendental equation of the first or second kind.
Masayoshi Tajiri, Shunji Kawamoto
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Theoretical and Mathematical Physics, 2001
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Approximate Solution of Space-Time Fractional KdV Equation and Coupled KdV Equations
Journal of the Physical Society of Japan, 2020The main goal of this article is to find the approximate solution of the space-time fractional order KdV (STFKdV) equation and Coupled KdV (STFCKdV) equations by using Homotopy analysis method (HAM...
Swapan Biswas +3 more
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Physics Letters A, 1998
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Modern Physics Letters B, 2021
This study is made to extract the exact solutions of Korteweg–de Vries–Burgers (KdVB) equation and Korteweg–de Vries (KdV) equation. The original idea of this work is to investigate KdV equation and KdVB equation for possible closed form solutions by employing the modified auxiliary equation (MAE) method.
Ghazala Akram +2 more
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This study is made to extract the exact solutions of Korteweg–de Vries–Burgers (KdVB) equation and Korteweg–de Vries (KdV) equation. The original idea of this work is to investigate KdV equation and KdVB equation for possible closed form solutions by employing the modified auxiliary equation (MAE) method.
Ghazala Akram +2 more
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Exact solutions for coupled KdV equation and KdV equations
Physics Letters A, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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PSEUDOPOTENTIAL METHOD APPLIED TO KdV EQUATION AND HIGHER DEGREE KdV EQUATION
Acta Mathematica Scientia, 1984Using the invariance of KdV equation under a Galilean transformation we obtain Newton's equation with the first approximation under the generalized meaning of a weak gravitation field, i.e. \[ (A)\quad \partial^ 2\phi /\partial x'{}^ 2=-\partial V(\phi)/\partial \phi \] where \(V(\phi)=(1/6)\phi^ 3-(1/2)v\phi^ 2-k\phi\) is called pseudopotential.
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2003
In this chapter we study small perturbations of the KdV equation $$ u_t = - u_{xxx} + 6uu_x $$ on the real line with periodic boundary conditions. We consider this equation as an infinite dimensional, integrable Hamiltonian system and subject it to sufficiently small Hamiltonian perturbations.
Thomas Kappeler, Jürgen Pöschel
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In this chapter we study small perturbations of the KdV equation $$ u_t = - u_{xxx} + 6uu_x $$ on the real line with periodic boundary conditions. We consider this equation as an infinite dimensional, integrable Hamiltonian system and subject it to sufficiently small Hamiltonian perturbations.
Thomas Kappeler, Jürgen Pöschel
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