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A search for bilinear equations passing Hirota’s three-soliton condition. II. MKdV-type bilinear equations. (English) Zbl 0658.35081
[For part I see ibid. 28, 1732-1742 (1987; Zbl 0641.35073).]
In this paper (second in a series) the search for bilinear equations having three-soliton solutions continues. This time pairs of bilinear equations of type $$P_ 1(D_ x,D_ t)F\cdot G=0$$, $$P_ 2(D_ x,D_ t)F\cdot G=0$$, where $$P_ 1$$ is an odd polynomial and $$P_ 2$$ is quadratic, are considered. The main results are the following new bilinear systems: $P_ 1=aD^ 7_ x+bD^ 5_ x+D^ 2_ x D_ t+D_ y,\quad P_ 2=D^ 2_ x;\quad P_ 1=aD^ 3_ x+bD^ 3_ 1+D_ y,\quad P_ 2=D_ xD_ t;$ and $P_ 1=D_ xD_ tD_ y+aD_ x+bD_ t,\quad P_ 2=D_ xD_ t.$ In addition to these, several models with linear dispersion manifolds were obtained, as before.

##### MSC:
 35Q99 Partial differential equations of mathematical physics and other areas of application
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##### References:
 [1] DOI: 10.1063/1.527815 · Zbl 0641.35073 [2] DOI: 10.1143/JPSJ.33.1456 [3] DOI: 10.1143/PTP.52.1498 · Zbl 1168.37322 [4] DOI: 10.1016/0375-9601(78)90444-9 [5] DOI: 10.1143/JPSJ.49.787 · Zbl 1334.35286 [6] DOI: 10.1143/JPSJ.33.1459 [7] DOI: 10.1143/JPSJ.49.771 · Zbl 1334.35282 [8] DOI: 10.2977/prims/1195182017 · Zbl 0557.35091 [9] DOI: 10.1143/JPSJ.48.1365 · Zbl 1334.35250 [10] DOI: 10.1143/JPSJ.52.744
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