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We consider numerical instability that can be observed in simulations of localized solutions of the generalized nonlinear Schr\"odinger equation (NLS) by a split-step method where the linear part of the evolution is solved by a…

Pattern Formation and Solitons · Physics 2014-10-15 Taras I. Lakoba

We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schr\"odinger equation with associated spectral data consisting of a single pair of conjugate poles of order $2n$. Starting from the zero…

Exactly Solvable and Integrable Systems · Physics 2019-05-01 Deniz Bilman , Robert Buckingham

A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector…

Mesoscale and Nanoscale Physics · Physics 2010-09-14 H. J. R. Westra , M. Poot , H. S. J. van der Zant , W. J. Venstra

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…

Pattern Formation and Solitons · Physics 2017-05-19 E. M. Gromov , B. A. Malomed , V. V. Tyutin

We study noise-induced perturbations of dispersion-managed solitons by developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber…

Pattern Formation and Solitons · Physics 2009-11-13 Jinglai Li , Elaine Spiller , Gino Biondini

We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the…

Pattern Formation and Solitons · Physics 2011-06-09 Valeriy A. Brazhnyi , Boris A. Malomed

Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped…

Pattern Formation and Solitons · Physics 2015-12-04 Evgeny M. Gromov , Boris A. Malomed

It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…

Exactly Solvable and Integrable Systems · Physics 2018-06-18 Antonio Degasperis , Sara Lombardo , Matteo Sommacal

Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical…

Pattern Formation and Solitons · Physics 2015-06-19 Goran Gligorić , Aleksandra Maluckov , Ljupčo Hadžievski , Boris A. Malomed

Nanoelectromechanical systems (NEMS) provide a platform for probing the quantum nature of mechanical motion in mesoscopic systems. This nature manifests most profoundly when the device vibrations are nonlinear and, currently, achieving…

Mesoscale and Nanoscale Physics · Physics 2025-04-15 M. Yuksel , M. P. Maksymowych , O. A. Hitchcock , F. M. Mayor , N. R. Lee , M. I. Dykman , A. H. Safavi-Naeini , M. L. Roukes

We report localized and unidirectional nonlinear traveling edge waves discovered theoretically and numerically in a 2D mechanical (phononic) topological insulator. The lattice consists of a collection of pendula with weak Duffing…

Pattern Formation and Solitons · Physics 2018-05-09 David D. J. M. Snee , Yi-Ping Ma

Shift manipulation of intrinsic localized mode (ILM) is numerically discussed in an ac driven Klein Gordon lattice. Before the manipulation, we introduce the 2-degree of freedom nonlinear system, which is obtained by reducing the lattice.…

Pattern Formation and Solitons · Physics 2023-12-11 Hirotaka Araki , Takashi Hikihara

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear…

Mesoscale and Nanoscale Physics · Physics 2023-04-05 Ata Keşkekler , Vincent Bos , Alejandro M. Aragón , Peter G. Steeneken , Farbod Alijani

We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schr\"{o}dinger (DNLS) equations with the self-attractive on-site self-phase-modulation nonlinearity, coupled by the repulsive…

Pattern Formation and Solitons · Physics 2022-07-11 Robert A. Van Gorder , Andrew L. Krause , Boris A. Malomed , D. J. Kaup

We analytically study nonlinear quasi-monochromatic plasma waves in a two-dimensional electron system set between the two metal electrodes (gates). We derive a nonlinear Schrodinger equation for a slow-varying envelope to describe the…

Mesoscale and Nanoscale Physics · Physics 2025-08-29 A. A. Zabolotnykh

The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by…

Analysis of PDEs · Mathematics 2021-08-05 Deniz Bilman , Robert Buckingham , Deng-Shan Wang

The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q$-nonextensive statistics.…

Plasma Physics · Physics 2016-01-05 D. Chatterjee , A. P. Misra

We investigate the localized waves of the coupled two-mode nonlinear Schr\"{o}dinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux…

Pattern Formation and Solitons · Physics 2013-09-30 Li-Chen Zhao , Liming Ling , Zhan-Ying Yang , Jie Liu

We consider a simple model system supporting stable solitons in two dimensions. The system is the parametrically driven damped nonlinear Schr\"odinger equation, and the soliton stabilises for sufficiently strong damping. The purpose of this…

Pattern Formation and Solitons · Physics 2009-11-10 N. V. Alexeeva

We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schroedinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken…

Pattern Formation and Solitons · Physics 2017-05-31 Zichao Wen , Zhenya Yan