The main objectives of this work are to deduce the Lax pair for Modified Toda lattice hierarchy and find whether there exists a transformation between (2+1)-dimensional derivative equation equation. By new spectral problem, we obtain hierarchy, furthermore give Hirota’s form solution equation, thus can also be attained correspondingly.

A similar type of nonlocal nonlinear Schrödinger (NLS) system arises in both water waves and nonlinear optics. The nonlocality is due to a coupling between the first harmonic and a mean term. These systems are termed nonlinear Schrödinger with mean or NLSM systems. They were first derived in water waves by Benney-Roskes and later by Davey-Stewartson. Subsequently similar equations were derived ...

Various classes of steady and unsteady dark solitary waves (DSWs) are known to exist in modulation equations for water waves in finite depth. However, there is a class of steady DSWS of the full water-wave problem which are missed by the classical modulation equations such as the Hasimoto-Ono, Benney-Roskes, and Davey-Stewartson. These steady DSWs, recently discovered by Bridges and Donaldson, ...

in this paper, the exp-function method, with the aid of a symbolic computation system such as maple, is applied to the (2+1) -dimensional calogero bogoyavlanskii schiff equation. exact and explicit generalized solitary solutions are obtained in more general forms. the free parameters can be determined by initial or boundary conditions. the method is straightforward and concise, and its applicat...

In this paper we continue studies of the functional representation of the Ablowitz– Ladik hierarchy (ALH). Using formal series solutions of the zero-curvature condition we rederive the functional equations for the tau-functions of the ALH and obtain some new equations which provide more straightforward description of the ALH and which were absent in our previous paper. These results are used to...