Bäcklund transformation and CRE solvability for the negative-order modified KdV equation
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DOI: 10.1007/s11071-017-3682-z
Abstract: The residual symmetry is obtained for the negative-order modified KdV (nmKdV) equation from the truncated Painlevé expansion by using symbolic computation. The multiple residual symmetries are presented and localized by introducing auxiliary variables, and then,… read more here.
Keywords: order modified; modified kdv; equation; cklund transformation ... See more keywords
A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions
Sign Up to like & getrecommendations! Published in 2018 at "Waves in Random and Complex Media"
DOI: 10.1080/17455030.2017.1367440
Abstract: Abstract A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified… read more here.
Keywords: integrable equation; modified kdv; equation; negative order ... See more keywords
Noncommutative negative order AKNS equation and its soliton solutions
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DOI: 10.1142/s0217732318502097
Abstract: A noncommutative negative order AKNS (NC-AKNS(-1)) equation is studied. To show the integrability of the system, we present explicitly the underlying integrable structure such as Lax pair, zero-curvature condition, an infinite sequence of conserved densities,… read more here.
Keywords: order akns; noncommutative negative; soliton solutions; equation ... See more keywords
Quasi-periodic solutions to a negative-order integrable system of 2-component KdV equation
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DOI: 10.1142/s0219887818500408
Abstract: In this paper, the backward and forward Neumann type systems are generalized to deduce the quasi-periodic solutions for a negative-order integrable system of 2-component KdV equation. The 2-component negative-order KdV (2-nKdV) equation is depicted as… read more here.
Keywords: periodic solutions; solutions negative; equation; negative order ... See more keywords
Neumann Type Integrable Reduction to the Negative-Order Coupled Harry–Dym Hierarchy
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DOI: 10.7566/jpsj.87.104004
Abstract: Based on the Lax compatibility, the negative-order coupled Harry--Dym (ncHD) hierarchy depending upon one parameter $\alpha$ is retrieved in the Lenard scheme, which includes the two-component Camassa--Holm (2CH) equation as a special member with $\alpha=-\frac14$.… read more here.
Keywords: order coupled; coupled harry; neumann type; hierarchy ... See more keywords