Linear superposition formula of solutions for the extended (3+1)-dimensional shallow water wave equation

Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model

“…[55], we have generalized the approach and investigated the effects of arbitrary spatio-temporal background ψ(z, t) background in the rogue waves and solitons for a (3+1)D Kadomtsev-Petviashvili-Boussinesq (KPB) equation. Next to that, there is another recent work [56] on kink-solitons for an extended (3+1)D shallow water wave equation with a similar ψ(z, t) background function. Following these exciting outcomes, in the present work, our aim is to study the influence of pure arbitrary two-dimensional spatial background in the evolution of lump and soliton, which shows different phenomena as explained in the forthcoming part of the manuscript.…”

“…Similarly, the dynamics of nonlinear waves on controllable backgrounds due to non-autonomous nonlinearities are explored in Bose-Einstein condensates too [6,[48][49][50][51][52]. Recently, some studies are reported for nonlinear wave structures in certain higher-dimensional nonlinear models describing shallow or deep water waves, which include the analyses of breathers in a variable-coefficient (3+1)D shallow water wave model [53,54], rogue waves and solitons on spatio-temporally variable backgrounds in (3+1)D Kadomtsev-Petviashvili-Boussinesq system [55], solitons in an extended (3+1)D shallow water wave equation [56], and interaction waves in both (3+1)D and (4+1)D Boiti-Leon-Manna-Pempinelli models [57,58] to name a few.…”

“…The above studies revealed different exciting results such as amplification, compression, bending/snaking, tunnelling/cross-over, superposed structures, etc. [5,6,[46][47][48][49][50][51][52][53][54][55][56][57][58]. So, it is our natural interest to question the possibility of realizing such phenomena in the above mentioned fifth-order nonlinear model (1).…”

Response reconstruction based on substructural condensation and modal-group superposition

“…This type of strategy was first presented by He et al [10] who decomposed a time-domain measurement signal into single-order modal responses that were transferred to the corresponding modal responses at inaccessible locations. The concept of superposing modal functions [11,12] was adopted to reconstruct the intact desired response. He et al [13] further reconstructed the stress and strain in the time domain using the Euler-Bernoulli beam theory.…”

Characteristics of dynamic waves in incompressible fluid regarding nonlinear Boiti-Leon-Manna-Pempinelli model

“…Equation (1.1) describes the interaction of a Riemann wave propagating along the y-axis and a long wave propagating along the x-axis in a fluid. The physical importance and reduction of this governing model to lower dimensions have been illustrated in worth-mentioning previous work [30,31]. Earlier, the (3 + 1)-dimensional nonlinear Boiti-Leon-Manna-Pempinelli model describing dynamical behavior of waves in incompressible fluid has been investigated by many researchers for appropriate solutions due to wide scientific importance.…”