Rogue wave solutions in nonlinear optics with coupled Schrödinger equations

Preventing critical collapse of higher-order solitons by tailoring unconventional optical diffraction and nonlinearities

“…(1) (see "Methods"). For the given expression of the sinusoidal square optical lattice (2), whose contour plot is portrayed in Fig. 1a, the corresponding band gap structure of Bloch-wave spectrum, as mentioned above, can be described and found by adopting the analogies with the solid energy band theory of crystalline materials and which, in the way as usual, should be based on the lowest (first) Brillouin zone of the lattice potentials.…”

“…Conversely, materials which exhibit different orders of nonlinearity, including the well-known cubic-quintic model with competing nonlinearities (self-focusing cubic and self-defocusing quintic nonlinear terms), can create stable multidimensional solitons and suppress the above-mentioned critical-and supercritical collapses 4,7,8,21,22 . Experimentally, fundamental solitons and vortex solitons in 2D and 3D geometries have been observed in CS 2 24,25 and in suspensions of metallic nanoparticles 26 . Theoretical predictions 27,28 and experimental observations [29][30][31][32] very recently confirmed the existence of stable multidimensional states of ultracold bosonic gases 8 , appearing as the so-called quantum droplets 27,28 , where the Bose-Bose mixture collapses are suppressed by quantum fluctuations 33 .…”

“…S olitons, alias localized waves, are stable objects balanced by diffraction/dispersion and nonlinearity [1][2][3] . The stable propagation and self-trapping of two-and three-dimensional (2D and 3D) solitons have recently received reinvigorating scientific interests in physics and beyond 4 .…”

Rogue Wave Solutions and Modulation Instability With Variable Coefficient and Harmonic Potential

“…The similarity transformation (ST) is utilized to construct the solutions. These waves are also found in deep and shallow water and, beyond oceanic expanses, in optical fibers [1][2][3][4][5][6][7][8], super fluids, and so on [9][10][11][12][13][14][15][16][17][18]. In recent times, the theoretical study of these kinds of waves has become an interesting part of the field of nonlinear sciences [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Soliton Solutions and Conservation Laws of a (3+1)-Dimensional Nonlinear Evolution Equation

“…Studying the nonlinear evolution equation arising in natural science is very important for us to understand and explain the nonlinear phenomena [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. By the analytical and numerical methods, many researchers constructed travelling wave solutions of some famous nonlinear mathematical physics equations, such as the nonlinear Schrödinger equation in nonlinear optics, the nonlinear Gross-Pitaevskii equation in the Bose-Einstein condensates, the Korteweg-de Vries (KdV) equation in fluid mechanics, and so on.…”