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¸÷λ³æÓÑÄãÃǺã¡ ÎÒÈ¥Äê12Ô·ÝͶÁËChaos, Solitons & FractalsһƪÎÄÕ£¬Ò»Ô·ݸøÁ˵ÚÒ»´ÎÐÞ¸ÄÒâ¼û£¬ÎÒÃÇÐ޸ĺóͶÉÏÈ¥£¬ÎÄÕÂÒ»Ö±´¦ÓÚunder review ״̬£¬µ½ÁË3ÔÂÖÐÑ®ÓÖÒ»´Î»ØÀ´ÐÞ¸ÄÒâ¼ûÈçÏ£¬´ó¼Ò¸øÎÒ·ÖÎöһϣ¬ÎÒÕâÆªÎÄÕ»¹ÓнÓÊܵÄÏ£ÍûÂð£¿ÎÒ4ÔÂÉÏÑ®Ð޸ĺóͶÉÏÈ¥£¬µ½ÏÖÔÚ»¹Ã»ÓÐÈκÎÏûÏ¢£¬´¦ÓÚunder review״̬¡£¼±ËÀÁË£¬ÎÒÄêµ×±ÏÒµ£¬Å±¾ßÁËÎÒ¾ÍÍêÁË¡£±ÏÒµÎÞÍûÁË¡£ Õâ´ÎÐÞ¸ÄÒâ¼ûÈçÏ£º To my regret, I have to inform you that I cannot accept your manuscript in its current form for publication. Although the problem that you are addressing appears to be of interest to our readership, I feel that your work has not yet reached the level that would merit publication in a scientific journal of high standards. I am offering you the opportunity to resubmit your work when you feel that your work has reached its final form. If you decide to do so, please explain carefully how you have modified your work in the cover letter. Note that our Aims & Scope have been revised recently. They may be found on the journal homepage: http://www.elsevier.com/locate/chaos. Further manuscript guidelines can be found in the Guide for Authors, which is accessible from the journal homepage. I would like to take this occasion to thank you for giving us the opportunity to consider your work. Reviewer's comments It is unsatisfactory revision: The reference on the work by Jimbo, Kruskal and Miwa explains which variant of the Painleve' is used in the paper. The sense of this test is to prove that the singular expansions (5)--(8) do represent the general solution of Equation (4) in the sense of the Cauchy-Kowalevsky theorem, i.e., to prove that these expansions depends on a proper number of the arbitrary functions depending on one variable, t. When we arrive at Equation(14) we can count three arbitrary real-valued functions of variable t, which is not enough, further analysis is not clearly presented. Still there is inaccuracy in the presentatiion, say on page 5, it is written that $\phi(t)$ is "an arbitrary analytical function", on the same page just below Equation (8) under the analytical function the authors mean complex analytic functions, but in case $\phi(t)$ is complex, Equations (6) and (8) should contain complex conjugate of $\psi(t)$, rather than just $\psi(t)$. Actually these expansions are written correctly because the function $\phi(t)$ is real. The latter is important for a proper counting of the number of arbitrary functions in the singular expansions (6)--(8). Equation (15) is not fully investigated, because in the case $4+F=(9-(2k+1)^2)/4$, for any integer $k$, there appear additional resonances that are not analysed. Something is wrong in Equation (19), since it does not represent any condition. It follows from the paper that Equation (33) should also pass the Painleve' test. At the same time there is a paper: R. RADHAKRISHNAN, R. SAHADEVAN, and M. LARSHMANAN, Integrability and Singularity Structure of Coupled Nonlinear Schroedinger Equations, Chaos. Solitons & Fractals Vol. 5, No. 12, pp. 2315-2327, 1995. Where the authors performs, in Section 3, the Painleve' test (in a very similar manner as in the present paper under review, of Equation (33). They report some special conditions on the coefficients of the cubic nonlinearity. So, I think that the results should be compared and reported to the readers, why some discrepancy occurs? In view of the paper by Deng-Shan Wang, Da-Jun Zhang, and Jianke Yang, Integrable properties of the general coupled nonlinear Schrodinger equations, J MATH PHYS, v 51, 023510 (2010), there might be that the results of the paper cited above are too restrictive. I also call attention to the work by Xing Lu, Juan Li, Hai-Qiang Zhang, Tao Xu, Li-Li Li, and Bo Tian, Integrability aspects with optical solitons of a generalized variable-coefficient N-coupled higher order nonlinear Schrodinger system from inhomogeneous optical fibers, J Math Phys 51, 043511 (2010). Only after the comparison of the results with that work we can seriously consider the paper for publication. I call attention that much more is known about explicit solutions of the coupled NLSE, so there should be also corresponding references and comments. Actually, the concluding part of the paper, I mean the part below Equation (34), is also not clear since it contains some heuristic statements. In view of the above report, I see that the paper is not ready to be considered for publication and should be rejected because of the insufficient quality. Sure, in case the authors will be able to work out all questions mentioned above and they see that there is still something new to report, they are welcome to resubmit the paper. |
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