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The most terrible thing is that it is very dangerous for sailors because it can appear unexpectedly and form larger amplitude in one minute to shred a boat. The key feature of the rogue wave is that it “appears from nowhere” and “disappears without a trace”. The amplitude of this wave is two to three times higher than those of its surrounding waves. The rogue wave is giant single wave which was firstly found in the ocean. The results can be used to study the matter rogue waves in the Bose-Einstein condensates and other fields of nonlinear science. In addition, the amplitudes of the rogue waves under the effect of the gravity field and external magnetic field changing with the time are analyzed by using numerical simulation.
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The first-order and second-order rogue waves solutions are obtained and the nonlinear dynamic behaviors of these solutions are discussed in detail. Google ScholarThe rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using the similarity transformation in this paper. Weinstein, The nonlinear Schrödinger equation-singularity formation, stability and dispersion, in "The Connection Between Infinite-Dimensional and Finite-Dimensional Dynamical Systems" (Boulder, CO, 1987), Contemporary Math., 99, Amer. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Venkov, Small data global existence and scattering for the mass-critical nonlinear Schrödinger equation with power convolution in $\R^3$, Cubo, 11 (2009), 15-28. Tsutsumi, Rate of $L^2$ concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power, Nonlinear Anal., 15 (1990), 719-724.ĭoi: 10.1016/0362-546X(90)90088-X. Strauss, Existence of solitary waves in higher dimensions, Comm. Ser., 43, Monographs in Harmonic Analysis, III, Princeton University Press, Princeton, NJ, 1993.
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Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals," With the assistance of Timothy S. Merle, Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two, Comm. Merle, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power, Duke Math. Lions, Solutions of Hartree-Fock equations for Coulomb systems, Commun. Lions, The concentration-compactness principle in the calculus of variations. Loss, "Analysis," Graduate Studies in Mathematics, 14, American Mathematical Society, Providence, RI, 1997.
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