EXACT ONE-PERIODIC AND TWO-PERIODIC WAVESOLUTIONS TO HIROTA BILINEAR EQUATIONS IN(2 + 1) DIMENSIONS

摘要

Riemann theta functions are used to construct one-periodic and two-periodic wave so-lutions to a class of (2 + 1)-dimensional Hirota bilinear equations. The basis for theinvolved solution analysis is the Hirota bilinear formulation, and the particular depen-dence of the equations on independent variables guarantees the existence of one-periodicand two-periodic wave solutions involving an arbitrary purely imaginary Riemann ma-trix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinearforms: ut+uxxg-3uuy -3u~xv=0 and ut+u_xxxxy - (5u_xxv+10u+xyu -15u~2v)_x=0where v_x =, thereby yielding their one-periodic and two-periodic wave solutionsdescribing one-dimensional propagation of waves.