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Travelling waves and conservation laws for complex mKdV-type equations

Please always quote using this URN: urn:nbn:de:0297-zib-16124
  • Travelling waves and conservation laws are studied for a wide class of $U(1)$-invariant complex mKdV equations containing the two known integrable generalizations of the ordinary (real) mKdV equation. The main results on travelling waves include deriving new complex solitary waves and kinks that generalize the well-known mKdV $\sech$ and $\tanh$ solutions. The main results on conservation laws consist of explicitly finding all 1st order conserved densities that yield phase-invariant counterparts of the well-known mKdV conserved densities for momentum, energy, and Galilean energy, and a new conserved density describing the angular twist of complex kink solutions.

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Author:Stephen Anco, Mohammad Mohiuddin, Thomas Wolf
Document Type:ZIB-Report
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX)
Date of first Publication:2012/10/17
Series (Serial Number):ZIB-Report (12-34)
ArXiv Id:http://arxiv.org/abs/1110.2403
ISSN:1438-0064
Published in:To appear in (accepted): Applied Mathematics and Computation
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