Abstract
We have undertaken the fact that the periodic solution of (2+1)D KdV-Burgers equation does not exist. The Saddle-node heteroclinic orbit has been obtained. Using the Lie group method, we get two-(1+1)-dimensional PDE, through symmetric reduction; and by the direct integral method, spread F-expansion method, and <svg style="vertical-align:-2.3205pt;width:47.662498px;" id="M1" height="20.6" version="1.1" viewBox="0 0 47.662498 20.6" width="47.662498" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,17.65)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,5.944,17.65)"><path id="x1D43A" d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242
q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" /></g> <g transform="matrix(.012,-0,0,-.012,18.25,9.488)"><path id="x2032" d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" /></g> <g transform="matrix(.017,-0,0,-.017,22.412,17.65)"><path id="x2F" d="M368 703l-264 -866h-60l265 866h59z" /></g><g transform="matrix(.017,-0,0,-.017,29.416,17.65)"><use xlink:href="#x1D43A"/></g><g transform="matrix(.017,-0,0,-.017,41.723,17.65)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g> </svg>-expansion method, we obtain exact nontraveling wave solutions, for the (2+1)D KdV Burgers equation, and find out some new strange phenomenons of sympathetic vibration to evolution of nontraveling wave.
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