@article{RosenauPikovskij2021, author = {Rosenau, Philip and Pikovskij, Arkadij}, title = {Waves in strongly nonlinear Gardner-like equations on a lattice}, series = {Nonlinearity / the Institute of Physics and the London Mathematical Society}, volume = {34}, journal = {Nonlinearity / the Institute of Physics and the London Mathematical Society}, number = {8}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0951-7715}, doi = {10.1088/1361-6544/ac0f51}, pages = {5872 -- 5896}, year = {2021}, abstract = {We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka-Volterra chain. Their deceptively simple form supports a very rich family of complex solitary patterns. Some of these patterns are also found in the quasi-continuum rendition, but the more intriguing ones, like interlaced pairs of solitary waves, or waves which may reverse their direction either spontaneously or due a collision, are an intrinsic feature of the discrete realm.}, language = {en} }