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In this paper we propose an efficient tomographic approach for the early detection of 2D rogue waves. The method relies on the principle of detecting conical spectral features before rogue wave becomes evident in time. More specifically,…

Fluid Dynamics · Physics 2017-03-10 Cihan A. Bayindir

In this paper, we use Hirota's bilinear method to directly construct periodic wave solutions of nonlinear equations. The asymptotic property of periodic wave solutions are analyzed. It is shown that well-known soliton solutions can be…

Exactly Solvable and Integrable Systems · Physics 2016-09-08 H. H. Dai , E. G. Fan X. G. Geng

We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave…

Pattern Formation and Solitons · Physics 2021-08-31 N. Sinthuja , K. Manikandan , M. Senthilvelan

Formation of giant waves in sea states with two spectral maxima, centered at close wave vectors ${\bf k}_0\pm\Delta {\bf k}/2$ in the Fourier plane, is numerically simulated using the fully nonlinear model for long-crested water waves [V.…

Fluid Dynamics · Physics 2015-05-13 V. P. Ruban

Breathers and rogue waves of special coupled nonlinear Schr\"odinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence.…

Pattern Formation and Solitons · Physics 2014-10-29 Jin Hua Li , Hiu Ning Chan , Kin Seng Chiang , Kwok Wing Chow

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…

Pattern Formation and Solitons · Physics 2015-06-23 H. Xu , P. G. Kevrekidis , A. Stefanov

We construct dark-dark solitons, general breather (GB), Akhmediev breather (AB), Ma soliton (MS) and rogue wave (RW) solutions of a coupled generalized nonlinear Schr\"odinger (CGNLS) equation. While the dark-dark solitons are captured in…

Exactly Solvable and Integrable Systems · Physics 2014-05-13 N. Vishnu Priya , M. Senthilvelan , M. Lakshmanan

We study fundamental rogue-wave solutions of the focusing nonlinear Schr\"odinger equation in the limit that the order of the rogue wave is large and the independent variables $(x,t)$ are proportional to the order (the far-field limit). We…

Exactly Solvable and Integrable Systems · Physics 2021-03-02 Deniz Bilman , Peter D. Miller

Families of solutions to the field equations of the covariant BRST invariant effective action of the membrane theory are constructed. The equations are discussed in a double dimensional reduction, they lead to a nonlinear equation for a one…

High Energy Physics - Theory · Physics 2009-10-30 A. Restuccia , R. Torrealba

We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a…

Exactly Solvable and Integrable Systems · Physics 2014-12-11 K. Sakkaravarthi , T. Kanna , M. Vijayajayanthi , M. Lakshmanan

We investigate the reduced Maxwell-Bloch (RMB) equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions. The general Nth-order periodic solutions are provided by means…

Exactly Solvable and Integrable Systems · Physics 2017-12-06 Jiao Wei , Xin Wang , Xianguo Geng

In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch(H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fibre and further generalize it to the matrix form of the $n$-fold…

Exactly Solvable and Integrable Systems · Physics 2013-01-28 Chuanzhong Li , Jingsong He , K. Porsezian

The soliton dressing matrices for the higher-order zeros of the Riemann-Hilbert problem for the $N$-wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Valery S. Shchesnovich , Jianke Yang

We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schr\"{o}dinger equation with third-order dispersion. This conceptually novel generation mechanism is based on…

In this paper, a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symbolic computation, lump and interaction solutions between lump…

Pattern Formation and Solitons · Physics 2020-10-27 Jian-Guo Liu , Wen-Hui Zhu , Yan He , Ya-Kui Wu

In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the…

Pattern Formation and Solitons · Physics 2022-06-22 M. Kirane , S. Stalin , M. Lakshmanan

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 V. S. Shchesnovich , J. Yang

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…

Quantum Physics · Physics 2009-11-10 A. D. Alhaidari

We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…

Pattern Formation and Solitons · Physics 2020-08-17 K. Sakkaravarthi , R. Babu Mareeswaran , T. Kanna

Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are…

Optics · Physics 2012-05-09 Guangye Yang , Lu Li , Suotang Jia