Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable Hénon-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivativ...

M Sawada, Y Kobayashi, Y Tanaka, C Shigemura, K Harada, H Tamura, H Tamura, M Matsumoto, H Asano, N Hagiwara, I Kitagawa, J Ikeda, Y Kido, A Higashi.* Graduate School of Life and Environmental Sciences, Kyoto Prefectural University, Kyoto, Japan; Kyoto Patisserie Art College, Kyoto, Japan; Kyoto College of Nutritional & Medical Sciences, Kyoto, Japan; Tamura Ladies Clinic, Kameoka, Japan; Depar...

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for exactly solvable potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gröbner bases method and others. New potentials and corresponding solutions of the Sawada–Kotera, Kaup– Kupershmidt, Boussinesq eq...

Nori NAKAMURA, Chuzo MIYAZAWA, Shozo SAWADA, Mitoshi AKIYAMA, A. A. AWA Department of Genetics and Department of Radiobiology, Radiation Effects Research Foundation, 5-2 Hijiyama Park, Minami-ku, Hiroshima 732, Japan, Department of Chemistry, Ohu University School of Dentistry, 31-1 Aza-Misumido, Tomita-machi, Koriyama 963, Japan, Department of Radiobiology, Research Institute for Radiation Bio...

Masaru Takeya, Fukuhiro Yamasaki, Shihomi Uzuhashi, Hiroyuki Sawada, Toshirou Nagai, Keisuke Tomioka, Toyozo Sato, Takayuki Aoki, Makoto Kawase Genetic Resources Conservation Research Unit, NIAS, Classification and Evaluation Research Unit, NIAS, Genetic Resources Center, NIAS A database of plant diseases in Japan was constructed and is available on the NIAS website. The database contains more...

In this paper, we study the possible second order Lax operators for all the possible (1+1)-dimensional models with Schwarz variants and some special types of high dimensional models. It is shown that for every (1+1)-dimensional model and some special types of high dimensional models which possess Schwarz variants may have a second order Lax pair. The explicit Lax pairs for (1+1)-dimensional Kor...

A method for symbolically computing conservation laws of nonlinear partial differential equations (PDEs) in multiple space dimensions is presented in the language of variational calculus and linear algebra. The steps of the method are illustrated using the ZakharovKuznetsov and Kadomtsev-Petviashvili equations as examples. The method is algorithmic and has been implemented in Mathematica. The s...

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