id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-6244	Ankit Dadhich	Symbolic Computational Algorithm for Hirota Bilinear Form to Higher-dimensional Nonlinear Partial Differential Equations in Nonlinear Sciences	2024	24	.pdf	application/pdf	8096	352	63	Substituting the trial solution u = eξi into the linear part of Eq. (18), namely utt − uxx − uxxx = 0, leads to the relation di = √ µ2i + µ4i . The higher-order derivatives become uyt = 2 (hxyth+ hxyht − hxthy − hxhyt)h 2 − 2hht(hxyh− hxhy) h4 , uxz = 2 (hxxzh+ hxxhz − 2hxhxz)h 2 − 2hhz(hxxh− h2x) h4 , uxx = 2 hxxxh 3 − 3hxhxxh 2 + 2h3xh h4 , uxy = 2 (hxxyh+ hxxhy − 2hxhxy)h 2 − 2hhy(hxxh− h2x) h4 , uxxxy = 2 hxxxy h − 2 hxxxxhy h2 − 8 hxxxyhx h2 − 8 hxxxhxy h2 + 16 hxxxhxhy h3 − 12 hxxhxxy h2 + 12 h2xxhy h3 + 36 hxhxyhxx h3 + 18 h2xhxxy h3 − 54 h2xhxxhy h4	cache/cana-6244.pdf	txt/cana-6244.txt