2021/10/28 by Boris A. Malomed, Malomed, Boris
Computer Science · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Liquid Crystal Research Advancements #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS) #Quantum Gases (cond-mat.quant-gas)
paper · pdf · doi:10.48550/arxiv.2110.14935
openalex publication_date 2021/10/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
A condensed review is presented for two basic topics in the theory of pattern\nformation in nonlinear dissipative media: (i) domain walls (DWs, alias grain\nboundaries), which appear as transient layers between different states\noccupying semi-infinite regions, and (ii) two- and three-dimensional (2D and\n3D) quasiperiodic (QP) patterns, which are built as superpositions of\nplane-wave modes with incommensurate spatial periodicities. These topics are\nselected for the present article, dedicated to the 70th birthday of Professor\nM. I. Tribelsky, due to the impact made on them by papers published by Prof.\nTribelsky and his coauthors. Although some findings revealed in those works may\nnow seem as "old" ones, they keep their significance as fundamentally important\nresults in the theory of nonlinear DW and QP patterns. Adding to the findings\nrevealed in the original works by M. I. Tribelsky et al., the present article\nalso reports several new analytical results, recently obtained as exact\nsolutions to systems of coupled real Ginzburg-Landau (GL) equations. These are:\na new solution for symmetric DWs in the bimodal system including linear mixing\nbetween its components; a solution for a strongly asymmetric DWs in the case\nwhen the diffusion (second-derivative) term is present only in one GL equation;\na solution for a system of three real GL equations, for the symmetric DW with a\ntrapped bright soliton in the third component; and an exact solution for DWs\nbetween counter-propagating waves governed by the GL equations with\ngroup-velocity terms. The significance to the "old" and new results collected\nin this review is enhanced by the fact that the systems of coupled equations\nfor two- and multicomponent order parameters, addressed in the article, apply\nequally well to modeling thermal convection, multimode light propagation in\nnonlinear optics, and binary Bose-Einstein condensates.\n