Deformations of third order Peregrine breather solutions of the NLS equation with four parameters
نویسنده
چکیده
In this paper, we give new solutions of the focusing NLS equation as a quotient of two determinants. This formulation gives in the case of the order 3, new deformations of the Peregrine breather with four parameters. This gives a very efficient procedure to construct families of quasirational solutions of the NLS equation and to describe the apparition of multi rogue waves. With this method, we construct the analytical expressions of deformations of the Peregrine breather of order N = 3 depending on 4 real parameters and plot different types of rogue waves.
منابع مشابه
Ten-parameters deformations of the sixth order Peregrine breather solutions of the NLS equation
In this paper, we construct new deformations of the Peregrine breather of order 6 with 10 real parameters. We obtain new families of quasi-rational solutions of the NLS equation. With this method, we construct new patterns of different types of rogue waves. We get as already found for the lower order, the triangular configurations and rings isolated. Moreover, one sees for certain values of the...
متن کاملDeformations of the seventh order Peregrine breather solutions of the NLS equation with twelve parameters
We study the solutions of the one dimensional focusing NLS equation. Here we construct new deformations of the Peregrine breather of order 7 with 12 real parameters. We obtain new families of quasirational solutions of the NLS equation. With this method, we construct new patterns of different types of rogue waves. We recover triangular configurations as well as rings isolated. As already seen i...
متن کاملHigher order Peregrine breathers solutions to the NLS equation
The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N + 1) in x and t. These solutions depend on 2N − 2 parameters : when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call PN breathers. Between all quasi-rational solut...
متن کاملRogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation
In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, th...
متن کاملRogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during ex...
متن کامل