By introducing and solving a new cross-constrained variational problem, a one-to-one correspondence from the prescribed mass to frequency of soliton is established for the generalized Davey-Stewartson system in two-dimensional space. Orbital stability of small soiltons depending on frequencies is proved. Multisolitons with different speeds are constructed by stable small solitons.

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This paper is concerned with the generalized Davey-Stewarston system in two dimensional space. Existence and stability of small solitons are proved by solving two correlative constrained variational problems and spectrum analysis. In addition, multi-solitons with different speeds are constructed by bootstrap argument.

By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schrödinger equations is found, and an open problem in normalized solutions is answered. Then existence and orbital stability of big solitons depending on frequencies for nonlinear Schrödinger equation with competitive power nonlinearity is proved for the first time. In addition multi-solitons of the equation with different speeds are constructed by stable big solitons.

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