User:Anjan.kundu/sandbox
Kundu-Eckhaus Equation
A generalization of nonlinear Schroedinger equation with additional quintic nonlinerity and a nonlinear dispersive term was proposed in [1] in the form
which may be obtained from the Kundu Equation (2), when restricted to <math>\alpha =0<math>. The same equation, limited further to the particular case <math>\beta =0,<math> was introduced later as Eckhaus equation, following which equation (3) is presently known as the Kundu-Ekchaus eqution. The Kundu-Ekchaus equation can be reduced to the nonlinear Schroedinger equation through a nonlinear transformation of the field and known therefore to be gauge equivalent integrable systems, since they are equivalent under the gauge transformation.
Properties and Applications
the Kundu-Ekchaus equation is asociated with a Lax pair, higher conserved quantity, exact soliton solution, rogue wave solution etc. Over the years various aspects of this equation, its generalizations and link with other equations have been studied. In particular, relationship of Kundu-Ekchaus equation with the Johnson's hydrodynamic equation near criticality is established[2] , its discretizations [3] , reduction via [[Lie symmetry]] [4] , complex structure via Bernoulli subequation [5] , bright and dark
- ^ Cite error: The named reference
Template:Kundu
was invoked but never defined (see the help page). - ^
Kundu, A. (1987), "Exact solutions in higher order nonlinear equations
gauge transformation", Physica D, 25: 399–406
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at position 54 (help) - ^ Levi, D.; Scimiterna, C. (2009), "The Kundu–Eckhaus equation and its discretizations", J. Phys. A
- ^ Toomanian; Asadi (2013), "Reductions for Kundu-Eckhaus equation via Lie symmetry analysis", Math. Sciences, 7: 50
- ^
Beokonus, H. M.; Bulut, Q. H. (2015), "On the complex structure of Kundu-Eckhaus equation via Bernoulli subequation
fungtion method", Waves in Random and Complex Media, 28 Aug.
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at position 79 (help)