Nonpropagating solitons of the variable coefficient and nonisospectral Korteweg-de Vries equation. (English) Zbl 0698.35141
Summary: The method of inverse scattering is extended to solve the initial value problem of a variable coefficient and nonisospectral Korteweg-de Vries equation with time varying boundary condition. One- and two-soliton solutions are examined in detail. By an appropriate decomposition, soliton interactions and asymptotic behaviors are investigated. Oscillating and asymptotically standing two-soliton solutions are discussed.
MSC:
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
References:
| [1] | DOI: 10.1103/PhysRevLett.52.1421 · doi:10.1103/PhysRevLett.52.1421 |
| [2] | DOI: 10.1007/BF00402138 · Zbl 0656.35138 · doi:10.1007/BF00402138 |
| [3] | DOI: 10.1103/PhysRevA.29.2370 · doi:10.1103/PhysRevA.29.2370 |
| [4] | DOI: 10.1088/0305-4470/19/18/003 · Zbl 0621.35086 · doi:10.1088/0305-4470/19/18/003 |
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