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Response to “Comment on ‘Generalized symmetry algebra of the conditionally integrable nonlinear evolution equation’ ” [J. Math. Phys. **40**, 3685 (1999)]

### Abstract

To verify the correctness of the high order symmetries for the Jimbo–Miwa–Kadomtsev–Petviashvilli system (JMKP) and the potential JMKP (PJMKP) system given in our paper [J. Math. Phys. **36**, 3492–3497 (1995)], Ma’s definition of may be used only for the general *nonkernel* solutions of the models. For some types of special solutions which are the kernels of some differential operators, one has to use as the indefinite operator and selected the integral functions appropriately.

© 1999 American Institute of Physics

Received 24 October 1998
Accepted 15 December 1998

/content/aip/journal/jmp/40/7/10.1063/1.532917

1.

1.W-x. Ma, “Comment on ‘Generalized symmetry algebra of the conditionally integrable nonlinear evolution equation,’ ” J. Math. Phys. 40, 3685 (1999).

2.

2.S-y. Lou and J-p. Weng, “Generalized symmetry algebra of the conditionally integrable nonlinear evolution equation,” J. Math. Phys. 36, 3492 (1995).

3.

3.H-y. Ruan and S-y. Lou, “Higher dimensional dromion structures: Jimbo–Miwa–Kadomtsev–Petviashvili system,” J. Math. Phys. 38, 3123 (1997).

4.

4.C-h. Gu, B-l. Guo, Y-s. Li, C-w. Cao, C. Tian, G-z. Tu, and M-l. Ge, Soliton Theory and its Application (Zhejiang, China, 1990), pp. 216–267.

http://aip.metastore.ingenta.com/content/aip/journal/jmp/40/7/10.1063/1.532917

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