"Mr. Cao, where are you in the office?" Xia Lu replied to a message while eating tea eggs in the cafeteria.

Cao Zhenggang: "Yes, are you up?"

Xia Lu: "I got up at 6 o'clock and was having breakfast in the cafeteria. Have you eaten, do you need to bring you breakfast?"

Cao Zhenggang: "Six fritters, eight meat buns, two cups of soy milk, thank you." Buy it and come over. ”

Wow, Mr. Cao has such an appetite.

After eating the tea eggs, Xia Lu bought fried dough sticks and meat buns and soy milk according to Mr. Cao's instructions.

At 7 o'clock in the morning, Mr. Cao was in the office, and he didn't eat breakfast.

What a diligent teacher.

Xia Lu carried the breakfast bag and came to Cao Zhenggang's office.

There are two people in the office, Cao Zhenggang and Yu Feng.

Even though the windows were open, the smell of smoke could still be smelled inside.

The ashtray was stuffed with cigarette butts, and two packs of cigarettes were visually consumed.

Everywhere there was paper, on tables, on chairs, on the ground.

Written on paper or by hand, or printed out mathematical-physical formulas.

The two professors' eyes were red, and they looked very tired, exhausted and excited, and the excitement contained a strange look.

Xia Lu put the breakfast bag on the table, and he couldn't help but ask, "You two worked here all night?"

"That's not the point, it's about you, Xia Lu. Cao Zhenggang grabbed a meat bun and wiped it out in an instant.

"Xia Lu, the plan you brought yesterday was completed by you alone?" Yu Feng killed two fritters with three strikes and five divisions, he was really hungry.

Xia Lu had long expected that the two teachers would ask such a question, and he said frankly: "I did it alone." ”

"Oh, you're pretty good, you can write a graduate-level thesis before you finish your freshman year. Cao Zhenggang stared at Xia Lu with blazing eyes, trying to find any clues from Xia Lu.

Xia Lu had already prepared the lines, and he said according to the lines he had designed: "Perhaps, I am more talented in science." ”

Yu Feng said: "Xia Lu, you are indeed a smart person, but you have shortcomings in dealing with specific problems, and the method you wrote has too many loopholes. You can't be blamed for that, after all, you're just a freshman. ”

"This ......" Xia Lu's heart chuckled, it shouldn't be, after I verified, the plan I gave did not have any loopholes, and I gave a brand-new, rigorous, and self-consistent method.

Am I wrong?

Or is the system wrong?

Or maybe you two teachers are wrong?

Wrong.

No, no, no, no.

The two teachers were testing my mental quality.

Xia Lu smiled, and responded to all changes with no change.

Cao Zhenggang pointed to the twentieth page of the method written by Xia Lu and said: "I have to say that Xia Lu, your ability to write this method in your freshman year shows that your level in mathematics and physics has far surpassed that of your contemporaries, and even surpassed some graduate students. Of course we are glad to have a student like you in our class. But there are also problems, for example, Xia Lu's adjoint equation and the solution of the conservation law of the fifth-order nonlinear equation you gave are not logically feasible. ”

"Can I explain my train of thought?" Xia Lu asked.

"Of course. The two teachers nodded.

Xia Lu walked to the blackboard, erased the contents of the blackboard, and then wrote a few formulas, saying: "I used the Ibragimov method to prove a lemma and give the conserved vector of the equation. ”

"Then, the general formula for the vector field is: V=ξ1(x,t,u)∂/∂t+ξ2(x,t,u)∂/∂x...... Two teachers, I think it should be rigorous and reasonable to prove this step, right?"

Cao Zhenggang gave a positive evaluation: "All the way to this point, it's no problem, in fact, this is also something that Teacher Yu and I have proven." The method you wrote, twenty pages ago, is different from our original plan in form, but the essence is the same. ”

"I guess what the two teachers said is logically unworkable, should mean the proof of the next conclusion?" Xia Lu looked at a formula on the blackboard and continued: "The two teachers said before that the CK direct method, the Buckran transform method, and the KK equation are not suitable for this topic, so we need to invent a new method based on NLPDEs. ”

So, I thought of Li Qun. Xia Lu paused at this point.

The two teachers said quietly, "Well, go on." ”

In order to be able to justify himself, Xia Lu used the last two months to study high-level knowledge including group theory and Li Qun.

The homework has been done, and now what Xia Lu has to do is to play normally: "Back to the last part of the method I wrote, if the vector field (3) is a Lie symmetry of equation (7), then V must satisfy such a Lie symmetry condition: prV(△)∣Δ=0=0. ”

"Yes, that's right, the question is here, Xia Lu, why do you want to do a fifth-order extension?" Yu Feng asked.

Xia Lu replied like a stream: "That's because, according to the above vector field, the Lie series formula of the optimal system can be deduced by using the fifth-order extension. Then by exchanging the subtable of the Lie series formula and the Lie algebra, we can continue to obtain the Lie algebra companion table......"

“…… After these operations are completed, the equation is reduced, and a new exact solution of the equation can be obtained by solving the reduced equation. ”

The above operations use all known mathematical and physical theories, and these known experiences are recombined to obtain a new method that is different from the CK direct method, the Buckran transform method, and the KK equation. ”

"I'm done, and I'm going to ask the two teachers to criticize and correct me. Xia Lukou Ruohanghe spoke for half an hour, and he thought that he had explained everything clearly.

Cao Zhenggang and Yu Feng glanced at each other and did not speak.

After a while, Yu Feng sighed with emotion: "There are talented people in the country, Xia Lu, you are a genius." ”

"Incredible, unbelievable. Cao Zhenggang said, "But I'm still very happy to see this genius appear in our class." ”

"So...... Is the method I wrote OK?" Xia Lu asked, and sure enough, the two teachers were deliberately looking for faults to test me.

"It's not just OK, it's just perfect!" Yu Feng slapped Xia Lu on the shoulder, he was very excited: "Regarding the new method you gave Xia Lu, Mr. Cao and I have already done a Maple verification, and the verification result is that vectors (C1, C2) are the conservation vectors of the core equation!"

"Great!" Xia Lu said with a smile, he was also very happy.

"So, we are now fully convinced that this method was done by Xia Lu alone. Cao Zhenggang looked at Xia Lu and said, "After you go back, Xia Lu, write your method again as quickly as possible according to the standard essay format." ”

Xia Lu nodded and said, "Well, okay, and then what?"

"Then?" the two teachers laughed, and then said, "Then Xia Lu, you kid is waiting to be famous!"