Vol.04 No.12(2014), Article ID:52798,1 pages
10.4236/apm.2014.412077

Erratum to “Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5)” [Advances in Pure Mathematics 4 (2014), 494-497]

Yoshikatsu Sasaki

Department of Mathematics, Hiroshima University, Higashi-Hiroshima, Japan   Received 1 June 2014; revised 3 July 2014; accepted 15 July 2014

The original online version of this article (Sasaki, Y. (2014) Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5). Advances in Pure Mathematics, 4, 494-497. http://dx.doi.org/10.4236/apm.2014.48055 ) was published in August, 2014. Unfortunately, it contains several mistakes. The author wishes to correct the following errors in  :

P. 494, L. 7-: The string equation of type (q, p) should be correctly read as P. 496, L. 13 - 14: Theorem B should be correctly read as follows:

Theorem B. The autonomous limit Equation (A) has a solution concretely described by the Weierstrass’ elliptic function as where or 3.

P. 496, L. 17: In Remark, g2 and g3 in the elliptic function theory should be correctly read as follows: P. 496, L. 21: In the r.h.s. of Equation (1), “ ” should be correctly read as “ ”.

P. 496, L. 3- - P. 497, L. 2: These 5 lines should be correctly read as follows:

If both of (2) and (3) are valid, then must vanish and coincides with 4 or .

Case and : In this case, we immediately obtain , , , where is a root of . Inversely, if these are sa-

tisfied, both of (2) and (3) are valid. can be reduced to by

. But, for brevity, now we put, and then, , i.e.

. Here and. The irrational equation satisfied by determines the

integral constant in the r.h.s. of (2) as.

Case and: In this case, we easily obtain, ,. Only is

allowed as the integral constant c in the r.h.s. of (2). Inversely, if these are satisfied, both of (2) and (3) are valid.

is reduced to by w = 3v, and then and. □

References

1. Sasaki, Y. (2014) Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5). Advances in Pure Mathematics, 4, 494-497. http://dx.doi.org/10.4236/apm.2014.48055