Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 36, Issue 9, Pages 2289-2303Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/36/9/307
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The known (2+1)-dimensional breaking soliton equation, the coupled KP equation with three potentials and a new (3+1)-dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the (1+1)-dimensional AKNS equations. The Abel-Jacobi coordinates are introduced to straighten out the associated flows, from which algebraic-geometrical solutions of the (2+1)-dimensional breaking soliton equation, the coupled KP equation and the (3+1)-dimensional evolution equation are explicitly given in terms of the Riemann theta functions.
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