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On the stabilization of the Korteweg–de Vries equation
Published 2010-09-01“…We consider the Korteweg–de Vries equation on a bounded intervalwith periodic boundary conditions. …”
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Weak damping for the Korteweg-de Vries equation
Published 2021-06-01“…For more than 20 years, the Korteweg–de Vries equation has been intensively explored from the mathematical point of view. …”
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Conservation Laws of Discrete Korteweg-de Vries Equation
Published 2005-12-01“…All three-point and five-point conservation laws for the discrete Korteweg-de Vries equations are found. These conservation laws satisfy a functional equation, which we solve by reducing it to a system of partial differential equations. …”
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Classical Solutions for the Generalized Korteweg-de Vries Equation
Published 2023-08-01“…The Korteweg-de Vries equation models the formation of solitary waves in the context of shallow water in a channel. …”
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Convergence of the Solutions on the Generalized Korteweg–de Vries Equation∗
Published 2016-03-01Subjects: Get full text
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Positive periodic solutions for the Korteweg-de Vries equation
Published 2007-04-01“…In this paper we prove that the Korteweg-de Vries equation $$ partial_t u+partial_x^3 u+upartial_x u=0 $$ has unique positive solution $u(t, x)$ which is $omega$-periodic with respect to the time variable $t$ and $u(0, x)in {dot B}^{gamma}_{p, q}([a, b])$, $gamma>0$, $gamma otin {1, 2, dots}$, $p>1$, $qgeq 1$, $a<b$ are fixed constants, $xin [a, b]$. …”
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Approximate solution of forced korteweg-de vries equation
Published 2002“…Several findings on forced solitons generated by the forced Korteweg de Vries equation (fKdV) are discussed in this paper. …”
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Numerical Simulation of the Korteweg–de Vries Equation with Machine Learning
Published 2023-06-01Subjects: Get full text
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Darboux transformation and solution of the modified Korteweg–de Vries equation
Published 2015-12-01Subjects: “…(2+1)-dimensional modified Korteweg-de Vries equation…”
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A nonlinear inverse problem of the Korteweg–de Vries equation
Published 2019-12-01Subjects: “…korteweg–de vries equation…”
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Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation
Published 2023-02-01Subjects: “…cylindrical Korteweg–De Vries equation…”
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