Semi-rational solutions of the third-type Davey-Stewartson equation
arXiv:1708.06304 · doi:10.1063/1.4999083
Abstract
General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions. It is shown that the fundamental (simplest) rogue waves are line rogue waves. It is also shown that the multi-rogue waves describe interactions of several fundamental rogue waves, which would generate interesting curvy wave patterns. The higher order rogue waves originate from a localized lump and retreat back to it. Several types of hybrid solutions composed of rogue waves, breathers and solitons have also been illustrated. Specifically, these semi-rational solutions have a new phenomenon: lumps form on dark solitons and gradual separation from the dark solitons is observed.
arXiv comment15 pages including 16 figures
References in corpus (17)
- Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
- General high-order rogue waves and their dynamics in the nonlinear Schroedinger equation
- Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
- A generating mechanism for higher order rogue waves
- Rogue waves in the Davey-Stewartson equation
- Financial Rogue Waves Appearing in the Coupled Nonlinear Volatility and Option Pricing Model
- Dynamics of rogue waves in the Davey-Stewartson II equation
- Non-Gaussian statistics and extreme waves in a nonlinear optical cavity
- Freak waves in the linear regime: A microwave study
- Rogue waves emerging from the resonant interaction of three waves
- High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
- Three-dimensional rogue waves in non-stationary parabolic potentials
- Optical Kerr Spatio-Temporal Dark-Lump Dynamics of Hydrodynamic Origin
- Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
- On the kurtosis of deep-water gravity waves
- Theoretical and experimental evidence of non-symmetric doubly localized rogue waves
- Rogue waves in nonlocal media
Cited by in corpus (5)
- Two (2 + 1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions
- Families of exact solutions of a new extended (2+1)-dimensional Boussinesq equation
- Dust ion-acoustic dromions in Saturn's magnetosphere
- On the stability of two-dimensional modulated electrostatic wavepackets in non-Maxwellian dusty plasma-application in Saturn's magnetosphere
- Appearing (disappearing) lumps and rogue lumps of the two-dimensional vector Yajima-Oikawa system