Stability of Big Solitons in a Competitive Power Nonlinear Schr\"odinger Equation

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. Mathematics Subject Classification (2010): 35Q55; 35J50; 37K40.

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