Doubly Periodic Wave Solutions and Soliton Solutions of Ablowitz–Ladik Lattice System |
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| Authors: | Wenhua Huang Yulu Liu |
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| Institution: | (1) College of Science, Huzhou University, Huzhou, 313000, China;(2) Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China |
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| Abstract: | The general Jacobi elliptic function expansion method is developed and extended to construct doubly periodic wave solutions
for discrete nonlinear equations. Applying this method, many exact elliptic function doubly periodic wave solutions are obtained
for Ablowitz–Ladik lattice system. When the modulus m→1 or m→0, these solutions degenerate into hyperbolic function solutions and trigonometric function solutions respectively. In long
wave limit, solitonic solutions including bright soliton and dark soliton solutions are also obtained. |
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| Keywords: | Ablowitz– Ladik system Jacobi elliptic function Soliton |
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