Author:
Mhadhbi Noureddine,Gana Sameh,Alsaeedi Mazen Fawaz
Abstract
AbstractThis paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical techniques such as the method of characteristics. Our primary focus is on NLPDEs of the form $$u_{tt}+a(x,t)u_{xt}+b(t)u_{t}=\alpha (x,t)+ G(u)(u_{t}+a(x,t)u_{x})e^{-\int b(t)dt}$$
u
tt
+
a
(
x
,
t
)
u
xt
+
b
(
t
)
u
t
=
α
(
x
,
t
)
+
G
(
u
)
(
u
t
+
a
(
x
,
t
)
u
x
)
e
-
∫
b
(
t
)
d
t
and $$u_{t}^{m}(u_{tt}+a(x,t)u_{xt})+b(t)u_{t}^{m+1}=e^{-(m+1)\int b(t)dt}(u_{t}+a(x,t)u_{x}) F(u,u_{t}e^{\int b(t)dt}).$$
u
t
m
(
u
tt
+
a
(
x
,
t
)
u
xt
)
+
b
(
t
)
u
t
m
+
1
=
e
-
(
m
+
1
)
∫
b
(
t
)
d
t
(
u
t
+
a
(
x
,
t
)
u
x
)
F
(
u
,
u
t
e
∫
b
(
t
)
d
t
)
.
We provide numerical validation through several examples to ensure accuracy and reliability. Our approach enhances the applicability of analytical solution methods for a broader range of NLPDEs.
Publisher
Springer Science and Business Media LLC
Reference40 articles.
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