TY  - JOUR
AU  - Pippal, Sarita
AU  - Vikramjeet
PY  - 2026
DA  - 2026/10/18
TI  - Polynomial-Based Kudryashov Analytical Methods for a Generalized Sharma–Tasso–Olver Equation with Non-Integer Nonlinearity
JO  - Journal of Numerical Simulations in Physics and Mathematics
T2  - Journal of Numerical Simulations in Physics and Mathematics
JF  - Journal of Numerical Simulations in Physics and Mathematics
VL  - 3
IS  - 1
SP  - 51
EP  - 59
DO  - 10.62762/JNSPM.2026.980251
UR  - https://www.icck.org/article/abs/JNSPM.2026.980251
KW  - generalized Sharma-Tasso-Olver equation
KW  - Kudryashov method
KW  - non-integer nonlinearity
KW  - travelling-wave solutions
KW  - solitary waves
AB  - We study travelling-wave solutions of the generalized Sharma-Tasso-Olver (GSTO) equation $u_t+\lambda(u^{r})_x+\mu(u^{s})_{xx}+\nu u_{xxx}=0$, in which the exponents $r,s>0$ need not be integers. The classical, modified and generalized Kudryashov methods are applied to the reduced ordinary differential equation. A balance argument shows that the convective term fixes the degree of the expansion through $N=2/(r-1)$, whereas the nonlinear diffusion term requires $N=1/(s-1)$; the two requirements are compatible only when $r=2s-1$, a condition satisfied by the classical STO equation ($r=3$, $s=2$). For the representative non-integer cases $(r,s)=(2,\tfrac32)$ and $(\tfrac32,2)$ we show that bounded solutions within the polynomial ansatz exist only in the dispersive limit $\mu=0$, and we derive them in closed form: a $\operatorname{sech}^2$ solitary wave for $r=2$ and a $\operatorname{sech}^4$ solitary wave with speed $\kappa=4\nu L^2$ for $r=\tfrac32$. The generalized Kudryashov method extends both results to hyperbolic, singular periodic and rational families classified by the discriminant $\Delta=\mathcal{B}_1^2-4\mathcal{B}_0\mathcal{B}_2$, with $\kappa=4\nu\Delta$ in the case $r=\tfrac32$. Every solution reported here was checked by direct substitution into the governing equation.
SN  - 3068-9082
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Pippal2026Polynomial,
  author = {Sarita Pippal and Vikramjeet},
  title = {Polynomial-Based Kudryashov Analytical Methods for a Generalized Sharma–Tasso–Olver Equation with Non-Integer Nonlinearity},
  journal = {Journal of Numerical Simulations in Physics and Mathematics},
  year = {2026},
  volume = {3},
  number = {1},
  pages = {51-59},
  doi = {10.62762/JNSPM.2026.980251},
  url = {https://www.icck.org/article/abs/JNSPM.2026.980251},
  abstract = {We study travelling-wave solutions of the generalized Sharma-Tasso-Olver (GSTO) equation \$u\_t+\lambda(u^{r})\_x+\mu(u^{s})\_{xx}+\nu u\_{xxx}=0\$, in which the exponents \$r,s>0\$ need not be integers. The classical, modified and generalized Kudryashov methods are applied to the reduced ordinary differential equation. A balance argument shows that the convective term fixes the degree of the expansion through \$N=2/(r-1)\$, whereas the nonlinear diffusion term requires \$N=1/(s-1)\$; the two requirements are compatible only when \$r=2s-1\$, a condition satisfied by the classical STO equation (\$r=3\$, \$s=2\$). For the representative non-integer cases \$(r,s)=(2,\tfrac32)\$ and \$(\tfrac32,2)\$ we show that bounded solutions within the polynomial ansatz exist only in the dispersive limit \$\mu=0\$, and we derive them in closed form: a \$\operatorname{sech}^2\$ solitary wave for \$r=2\$ and a \$\operatorname{sech}^4\$ solitary wave with speed \$\kappa=4\nu L^2\$ for \$r=\tfrac32\$. The generalized Kudryashov method extends both results to hyperbolic, singular periodic and rational families classified by the discriminant \$\Delta=\mathcal{B}\_1^2-4\mathcal{B}\_0\mathcal{B}\_2\$, with \$\kappa=4\nu\Delta\$ in the case \$r=\tfrac32\$. Every solution reported here was checked by direct substitution into the governing equation.},
  keywords = {generalized Sharma-Tasso-Olver equation, Kudryashov method, non-integer nonlinearity, travelling-wave solutions, solitary waves},
  issn = {3068-9082},
  publisher = {Institute of Central Computation and Knowledge}
}