Resonance dynamics of kinks in the sine-Gordon model with impurity, external force and damping

Changing the Dynamic Parameters of Localized Breather and Soliton Waves in the Sine-Gordon Model with Extended Impurity, External Force, and Decay in the Autoresonance Mode

“…However, the (1+1)-dimensional models are the most studied. For some applications, it is necessary to account for dissipation and external force in the system (e. g., [1][2][3][10][11][12][13][14]). Parameters of SGE are also often set as functions of coordinates and time [15][16][17][18][19][20].…”

“…However, it is more often necessary to use numerical methods [1-3, 13-15, 22, 23]. Many numerical methods for these equations have been developed [9,13,14,[26][27][28][29][30].…”

Excitation of Large-Amplitude Localized Nonlinear Waves by the Interaction of Kinks of the Sine-Gordon Equation with Attracting Impurity

“…The effect of small perturbations on the SGE solutions can be studied using a well-developed perturbation theory for solitons [5,19,20]. The effect of perturbations can generally be investigated only with the help of numerical methods [20][21][22][23]. For example, the influence of a coordinate-and time-dependent external force has been studied [24][25][26].…”

“…The importance of impurity modes in the kink dynamics was shown in [5,28,36]. The structure and properties of localized nonlinear waves excited on an impurity were analyzed numerically in [21,23,32]. The case of several point impurities that are of interest in some physical applications was considered in [44] and even the case of spatially modulated harmonic potential was considered [31].…”

Magnonic band spectrum of spin waves in an elliptical helix

“…In the context of magnonics (the study of spin waves) and magnonic devices, major research efforts have been devoted to investigation of spin waves [11,12] in curved (or otherwise shaped) magnonic waveguides [13][14][15][16][17][18][19][20][21][22][23][24][25]-ubiquitous elements of any magnonic logic architecture [26]-and more generally in non-uniform magnetic configurations [27][28][29][30][31][32][33][34][35][36][37][38]. The growing variety of proposed magnonic devices and architectures [39][40][41][42][43][44] ( [45] and references therein) [46][47][48] requires that the nature and diversity of mechanisms of scattering of spin waves in topologically complex magnetic media and graded magnonic landscapes [49][50][51][52][53][54] be properly understood.…”