Modulation instability and rogue waves for the sixth-order nonlinear Schrödinger equation with variable coefficients on a periodic background

نویسندگان

چکیده

In this paper, rogue wave solutions of a sixth-order focusing nonlinear Schrödinger (NLS) equation with variable coefficients are investigated on periodic background. To get the results, we take advantage Darboux transformation approach and nonlinearization spectral problem firstly find one kind solution that evolves periodically time spatial Besides, also dissipates over time. Modulation instability (MI) NLS is studied.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Periodic waves of a discrete higher order nonlinear Schrödinger equation ∗

The Hirota equation is a higher order extension of the nonlinear Schrödinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete per...

متن کامل

Dynamics of Rogue Waves on a Multisoliton Background in a Vector Nonlinear Schrödinger Equation

General higher order rogue waves of a vector nonlinear Schrödinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free parameters are expressed in separation of variables form. These solutions exhibit rogue waves on a multisoliton background. They demonstrate that the structur...

متن کامل

Rogue waves and rational solutions of the nonlinear Schrödinger equation.

We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work can elucidate the appearance of rogue ...

متن کامل

Rogue 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 کامل

Rogue periodic waves of the mKdV equation

Rogue periodic waves stand for rogue waves on the periodic background. Two families of traveling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and twofold Darboux transformations, we construct explicitly the rogue periodic waves of the mKdV equation. Since the dn-periodic wave i...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Nonlinear Dynamics

سال: 2022

ISSN: ['1573-269X', '0924-090X']

DOI: https://doi.org/10.1007/s11071-022-07538-9