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On the evolution of a rogue wave along the orthogonal direction of the (t, x)-plane

2016; Elsevier BV; Volume: 44; Linguagem: Inglês

10.1016/j.cnsns.2016.08.012

1878-7274

Feng Yuan, Deqin Qiu, Wei Liu, K. Porsezian, Jingsong He,

Ocean Waves and Remote Sensing

The localization characters of the first-order rogue wave (RW) solution u of the Kundu–Eckhaus equation is studied in this paper. We discover a full process of the evolution for the contour line with height c2+d along the orthogonal direction of the (t, x)-plane for a first-order RW |u|2: A point at height 9c2 generates a convex curve for 3c2 ≤ d < 8c2, whereas it becomes a concave curve for 0 < d < 3c2, next it reduces to a hyperbola on asymptotic plane (i.e. equivalently d=0), and the two branches of the hyperbola become two separate convex curves when −c2<d<0, and finally they reduce to two separate points at d=−c2. Using the contour line method, the length, width, and area of the RW at height c2+d(0<d<8c2) , i.e. above the asymptotic plane, are defined. We study the evolutions of three above-mentioned localization characters on d through analytical and visual methods. The phase difference between the Kundu–Eckhaus and the nonlinear Schrodinger equation is also given by an explicit formula.