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Homoclinic breather-wave solutions and doubly periodic wave solutions for coupled KdV equations. (English) Zbl 1231.35215

The paper aims at obtaining exact solutions for a Korteweg-de Vries equation nonlinearly coupled to an extra linear equation, \[ u_t+\alpha u_{xxx} -buu_x +cvv_x=0, \]
\[ v_t + dv_{xxx} - euv_x +fu_xv = 0. \] It was shown in previous works that this system admits a large variety of exact solutions in certain particular cases. In this work, the Painlevé expansion and analysis of homoclinic trajectories are employed to obtain exact two-cycle breather solutions, and also double-periodic solutions, in terms of elementary trigonometric functions. Possible physical realizations of such solutions are discussed.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35L75 Higher-order nonlinear hyperbolic equations
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