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Based on the Hirota bilinear method and the Riemann theta function, a straightforward way is shown to construct quasi-periodic wave solutions of supersymmetric equations. The resulting theory is applied to the supersymmetric modified Korteweg–de Vries equation. Further, we analyze the asymptotic properties of the solutions and give their asymptotic relations between the quasi-periodic wave solutions...
Staring from a new spectral problem, a hierarchy of the soliton equations is derived. It is shown that the associated hierarchies are infinite-dimensional integrable Hamiltonian systems. By the procedure of nonlinearization of the Lax pairs, the integrable decomposition of the whole soliton hierarchy is given. Further, we construct two integrable coupling systems for the hierarchy by the conception...
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