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arxiv: 1110.3247 · v1 · pith:SPFYILVBnew · submitted 2011-10-14 · 🌊 nlin.SI · math-ph· math.MP

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

J. F. Gomes , Guilherme S. Fran\c{c}a , A. H. Zimerman This is my paper
classification 🌊 nlin.SI math-phmath.MP
keywords hierarchysolitonsboundaryequationgardnermkdvnonvanishingsolutions
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A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is proposed. Solutions are systematically constructed employing the dressing method and deformed vertex operators which takes into account the nonvanishing boundary value problem for the mKdV hierarchy. Explicit examples are given and besides usual KdV like solitons, our solutions contemplate the large amplitude table-top solitons, kinks, dark solitons, breathers and wobbles.

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    New soliton solutions for Chen-Lee-Liu and Burgers hierarchies are derived via dressing methods on zero and non-zero vacua, classified by vertex operators, and extended by gauge-Bäcklund transformations.